You get the quest "Season Unending" while doing the quest "The Fallen". The Jarl of Whiterun will only agree to help you out and offer his palace as a trap to the dragon, if you can negotiate a peace truce between Tullius and Ulfric Stormcloak. The main quest "The Fallen" cannot advance until you are done with "Season Unending"

Open your quest journal:
Season Unending
The Jarl of Whiterun won't help me capture a dragon as long as the civil war is raging. If I can get the Greybeards to host a peace council, I can try to convince the Imperials and the Stormcloaks to agree to a truce in order to defeat Alduin, who is a threat to both sides in the civil war.

Talk to Arngeir

Fast travel to High Hrothgar and locate Arngeir, most likely meditating in the High Horthgar courtyard. He will tell you he heard the dragonrend shout from there and asks you if you defeated him. Tell him that yes, but he escaped and you need to find his portal to Sovngarde. Tell him you need his help to capture a dragon. He tells you the Greybeards are not warrriors, and while the Dragonborn is allowed to fight, the Greybeards aren't. Tell him not to worry about catching the dragon, you will do that. What you need his help with is stopping the war. He will tell you that you misunderstand their authority. The Greybeards have never involved themselves in political affairs.

Tell him that Jarl Balgruuf won't help you while the war rages. And that both sides respect Greybeards, and will listen. He will say that since Paarthurnax has made the decision to help you, this is the road they have to walk. (Dialog will be different if you have slain Paarthurnax).

He will agree to host the peace summit. He will ask you to tell General Tullius and Ulfric that the Greybeards wish to talk with them together. You have to deliver the message to the warring parties.. If they will listen, Arngeir will do whatever he can to bring them to terms.

Open the quest log:
"Arngeir has agreed to host a peace council at High Hrothgar. I need to convince the Imperials and the Stormcloaks to agree to a truce in order to defeat Alduin, who is a threat to both sides in the civil war"

Talk to Ulfric Stotmcloak
Talk to General Tullius

General Tullius can be found in Solitude. Fast travel there (or hire a carriage). Enter Castle Dour. Locate the war room inside. Legate Rikke is there warning Tullius about Ulfric's plans to attack Whiterun. Talk to Tullius. Tell him you were at Helgen. he will remember you were a prisoner. Tell him you were set free and could've gone anywhere, but came here to fight for the Empire. Then talk to him again and tell him you have a message from the Greybeards. They are convening a peach council at High Hrothgar. Tell you you need a truce until the dragon menace is dealt with. PERSUADE him that the dragons are bigger problem then Stormcloaks right now. If the persuasion fails, he tells you that he will be the judge of that. The Stormcloaks are suffering from the dragons just as much as the Imperials are.

Tell him the empire can't afford to snub the Greybeards. He will see your point and agree to come to this Greybeard council.

Next, go to Windhelm. Enter the palace of the kings. Galmar and Jarl Ulfric Stormcloak are also discussing the war and Whiterun. He also remembers you from Helgen. He tells you to speak with Galmar if you want to join the Stormcloaks. Tell Ulfric you have a message from the Greybeards, they wish to negotiate a truce until the dragon menace is dealth with. He will have some doubts, he cant afford to be weak. He will only go if Tullius has agreed to go. If you have already convinced General Tullius to come, tell him that Tullius will be there. Otherwise try to persuade him, saying the return of Alduin is more important then politics. Ulfric Stormcloak will agree to come to the peace council.

Your goal now is to talk to Arngeir again. Fast Travel to High Hrothgar and talk to Arngeir. Delphine and Esbern have shown up, and are arguing with Arngeir who tells them they are not welcome. They say they have the right to be there since they put the dragonborn on the path. Esbern explains that they know a  great deal about Alduin and the threat he poses. For the negotiations to succeed, you need them there. Arngeir will finally agree they enter. Arngeir will express his concerns that men of violence are sitting in this hall of peace and that he should not have agreed to that. Tell him not to worry, you'll get them to agree to peace. Enter the Grand Hall and take your seat. Negotiations will begin.

Attendants are:
Legate Rikke (Imperials)
Jarl Elisif  of Solitude (Imperials)
General Tulius (Imperials)
Jarl Balgruuf (Imperials)
Ulfric Stomrcloak (Stormcloaks)
Galmar Stone-Fist (Stromcloaks)
Jarl Vignar of Whiterun (Stormcloaks) (Optional)
Elenwen (Thalmor Observer)

Elenwen will say she has the right to be here to see that nothing agreed here goes against the white-gold concordat. As the negotations progress, certain dialog options will favor a faction. If you have already joined a faction you might want to choose the dialogs that please them, otherwise they will be upset at you in the end. We provide the walkthrough for the negotiations and also list what happens if you take the other option. We also tell you which option favors the imperials, and which favors the Stormcloaks. So be sure to consult with this negotiation guide as you conduct the peace negotiations.

The first order of business: The Imperials have included Elenwen, the Thalmor Ambassador, in their delegation. Your first decision will be whether to let Elenwen stay or whether to kick her out of the meeting, as demanded by Ulfric. He refuses to sit at the table with Elenwen. Either she walks, or he does.

What's the harm? Beside, Tullius doesn't want her here either (Favor Imperials)
You are right, the Thalmor has no business here. (Favor Stormcloaks)

Choose to let her stay. Ulfric will reuctantly agree but demand she only observe not directly participate in the negotiations. Elenwen will ask Ulfric why he is so hostile about the Thalmor. It is not them that are burning his farms and killing his sons.

Ulfric will give a speech on how he is only there to negotiate a temporary truce to help the Dragonborn, but nothing more, unless the empire is truly ready to renounce their unjust claim to rule over the free people of Skyrim. He considers even talking to the empire a generous gesture. 

Arngeir will begin conducting the negotiations. Jarl Ulfric, General Tullius - This council is unprescendeted. We are all hear at the Dragonborn's request. All should respect the spirit of high Hrothgar and respect the will to achieve a lasting piece in Skyrim. He will ask who would like to begin the negotiations.

The next item in the negotation is the exchange of a major hold. Either the Stormcloaks will demand to get Markarth to their side, or the Imperials will demand Riften to be transferred under their control. The other side will be outraged. Legate Rikke will blame Ulfric in insulting the Greybeards by using the peace council to advance his own position. Elisif will also protest of handing over Markarth to that traitor. Tullius will say he will handle it. Arngeir will say that surely Ulfric doesnt expect something for nothing. Tullius will clarify that this council was not his idea and he personally thinks its a waste of time. He will accuse Ulfric of being a traitor to the empire, and deserving a traitor's death. But he at least negotiates in good faith. General Tullius asks you what you think Markarth is worth.

Markarth is a major hold for the Imperials, so reply accordingly:

You can say:
How about Riften? (Favor Imperials. Riften is a major hold)
Winterhold  seems like a fair trade (Favor Stormcloak, as winterhold is a minor hold)

Say Riften, since that trade is more fair. Tullius agrees that the Rift would help secure their communications with Cyrodiil and threaten Ulfric's southern flank.

Ulfric will be furious. He expected better from the Dragonborn then to help the Empire at every turn. He stands up and threatens to leave. Tullius tells Ulfric he was always a fool, that he is no better in diplomacy then he is on the battlefield.

If instead you were to say Winterhold (Minor Hold) is  a fair exchange for Markarth, General Tullius will be upset. Markarth is a major source of Skyrim's silver. Exchanging it for a small hold like Winterhold is clearly not fair. Riften seems like a more fair trade to him, easily resupplied, across from the river. You can say he asked for your opinion so you gave it to him, or you can try and PERSUADE him that there are advantages to be gained by holding Winterhold. But he will say it's not enough to outweigh the loss of Markarth. With the reach at the Stormcloak's hands, Solitude will be in danger. He will blame you that you are biased and a part of Ulfric's camp. But he will see that holding Winterhold would allow them to threaten the rebel supply lines out of Windhelm.

Esbern will stop them and give a speech. Are they so petty in their disagreements that they don't see the real threat? They are arguig about nothing while the fate of the lands lie on the balance. Delphine advices both sides to listen to what they have to say. The world eater has returned. He grows more powerful with every soldier slain in the war, for he devours on the soul of the dead. The speech will convince Ulfric to come back to the negotiation table. But he still is not happy with the terms. He wants Hjaalmarch to be surrendered to the Stormcloaks. He will tell you to decide:

I agree, the Empire should turn over Hjaalmarch (Favor the Stormcloak)
The Empire doesn't need to give any more territory (Favor the Imperials)

Since you surrendered Markarth in exchange for Riften, which was already a fair trade, you should say that the Empire doesn't need to give any more territory. Ulfric will be upset but will agree for the good of Skyrim.

If you had favored the Stormcloaks previously over the Empire, now the empire will demand compensation for the Massacre at Karthwasten. But Ulfric will deny the accusations about the massacre and tell Tullius that all the blood was on his hands. They will also want the Pale return to the Imperial's control.

Arngeir will declare that they have an agreement and read the terms of the negotations that were agreed. Markarth would be handed over to the Stormcloaks and the Jarl will step down. Stormcloaks will withdraw from the Rift and allow the imperials unhindered access. Maven Black-Briar will become the Jarl of Riften. He will ask if both parties agree to this. They both will replay that they can live with those terms until the Dragon Alduin is slain. Tullius will comment that Markarth was a heavy price to pay for the truce and that he hopes it is worth it.

Arngeir will turn to the Jarl of Whtiterun and ask him if he remembers the plan to trap the dragon. The Jarl will reply that he is ready to do his part. Just say the word, and his men will spring the trap. The difficulty remains, how to lure a dragon to Dragonsreach in the first place? Esbern will say he has a solution. He has identified one of the dragons that Alduin has raised from the dead. Ask him how it helps you. He will say that the names of dragons are always 3 words of power, shouts. If you shout them, he will hear you, wherever he might be. Ask him why would he come when called. He will say that dragons are proud by nature and won't refuse a challenge. Your voice will intrigue the dragon, especially after your victory over Alduin. It is very likely that the dragon will be unable to resist your call. Ask him what the dragon's name is. It is "Od Ah Viing", or Winged Snow Hunter. He hands you over a scroll, and you learn the following shout:

Word of Power: Snow, Call Dragon
Word of Power: Hunter, Call Dragon
Word of Power: Wing, Call Dragon

If you haven't talked to Esbern or Delphine since completing Alduin's Bane, Delphine now approaches you. There is a problem. They have learned who the Greybeards leader is. Paarthurnax, the dragon that the Greybeards have been protecting all these years. Paarthurnax  helped Alduin enslave their ancestors. He needs to die and it falls to you to kill him.  This opens up the quest to kill Paarthurnax, which is an optional quest. If you kill Paarthurnax, you will lose the support of the Greybeards. If you don't kill him, you will lose the support of the Blades. Refer to the Paarthurnax Quest Walkthrough for more information.

The quest description for Season Unending has updated:
"The Jarl of Whiterun wouldn't help me capture a dragon as long as the civil war was raging. Arngeir agreed to host a peace council at High Hrothgar. With Esbern's help, I persuaded General Tulius and Ulfric Stormcloak to agree to a truce in order to defeat Alduin, who is a threat to both sides in the civil war"

This completes the quest "Season Unending". You now go back to Whiterun to proceed with the quest "The Fallen"