When you get close enough to her, Serana and Valerica will start up a conversation, and you'll learn that Serana's blood is required for Harkon's prophecy, which Valerica will refer to as the Tyranny of the Sun. You'll find her in a prison to the northeast (#10). The first thing you'll need to do in this quest is track down Serana's mother Valerica.
To open the gates, you'll need to shoot something (either an arrow or spell) through the lights. In a few places you'll also find closed gates with two glowing blue lights (usually in standing stones) nearby. Harvesting these will fill your most powerful empty soul gems with a soul. Most of these souls won't say or do much, but three of them (#1, #4, and #7) will give you quests or tasks to complete. These enemies will drop soul gems and more when they die. As you explore it, you'll encounter many interesting things, including:
You'll receive this quest when you enter the Soul Cairn (at Exit A) at the conclusion of the quest