Speak to Serana. Ask her what's on her mind. She talks about what the Moth Priest, Dexion, said. Serana thinks she knows where to start looking for the two other Elder Scrolls. She did not reveal this to Harkon earlier since she believes he is too obsessed with the prophecy. She says that we need to find her mother, Valerica. Valerica will definitely know where it is, and if we are lucky, she actually has it herself. The last time Serana saw her mother, she said that she'd go somewhere safe, somewhere that Harkon would never search. But Serana can't imagine a single place Harkon would avoid looking, especially when he has had all this time.

Your choices are:
Hiding with the Dawnguard
Sealed away like you were?
How about right here, in the castle?

If you choose the first option, Serana says that she doubts her mother would waste her time with those fools. The Dawnguard would probably try to kill her anyway. She also does not believe her mother would want to be sealed away like Serana was.

Suggest to her that her mother could be hiding right here in he castle. Serana says it almost makes sense. She used to help her mother tend a garden in the courtyard here. All of the ingredients for the potions came from there. Her mother used to say that Harkon couldn't stand that place, it was too peaceful.

Ask Serana how to get in without Harkon noticing. Serana says that there is an unused inlet on the northern side of the island that was used by the previous owners to bring supplies into the castle. An old escape tunnel from the castle exits there. That's your way in.

When you are ready, tell her that you should both go to the castle's secret entrance. Your objective updates. Check your quest log:

Chasing Echoes
Serana has indicated her desire to locate her estranged mother, Valerica, who had fled castle Volkihar with one of the Elder Scrolls. She believes that Valerica may have left a clue to her whereabouts somewhere in the courtyard of the castle. In order to avoid detection by Harkon, we've decided to utilize a secret entrance on the back side of the island

Skyrim Dawnguard Castle Volkihar Secret Entrance

Explore Castle Volkihar's Courtyard

Exit the castle. Standing on the bridge, facing away from the castle, jump off the ledge to your right. You can either climb the mountains and approach the secret entrance from above, or you could drop onto the water and swim around the island. There will be skeletons guarding the entrance. Kill them, then climb the stairs and enter through the door into the Volkihar Undercroft.