The female vampire in Dimhollow Cavern introduces herself as Serana.

You have some new dialog options:
Any idea how to get out of here?
Is that an Elder Scroll?
Tell me about your home
How long where you in there?
Why were you locked away?

If you ask her how to get out of here, she does not know. The place looks very different from when she was first locked away.

If you ask her about the scroll she is carrying on her back, she tells you that yes it is an Elder Scroll and it is hers. You can then ask her:
Why do you have an Elder Scroll?
Is it fragile? Do we need to be careful with it?

Ask her the reason for carrying the Elder Scroll around, but she says it is complicated. If you are worried that the Elder Scroll is fragile, she assures you that nothing can destroy an Elder Scroll.

You can ask her to tell you more about her home. She says it is on an island near Solitude, and that hopefully you can find a boat to take you there. It's her family home. Not the most welcoming place, but depending on who's around, she will be safe there.

You can ask:
Why wouldn't you be safe there?
Someone you don't want to see?

She tells you that her mother and father had a bit of a falling out. She is not in any danger, but it would just be more unpleasant to run into her father.

If you ask her how long she has been locked in here, she tells you it is hard to say. It was a long time. She asks you who Skyrim's High King is. You can tell her:
That's actually a matter for debate
Ulfric Stormcloak is the true High King
Elisif of Solitude will be High Queen

She asks about the contenders. You tell her that the Empire from Cyrodiil supports Elisif, but there are many in Skyrim loyal to Ulfric. She did not know that Cyrodiil is a seat of the Empire, so she deduces that she must have been here longer than she thought.

You can ask her why she was locked away here, but she would rather not get into it. She does not know if she can trust you yet.

If you offer to trade some things with her, she refuses.

Once you are done exploring all the dialog options, your new objective is to lead Serana to her home. Time to exit the caverns.