Birth By Sleep takes place about 10 years before the original Kingdom Hearts. Before Sora wielded the Keyblade, there were other Keyblade masters. One of these masters, Xehanort, disappeared one day along with his apprentice. Another master of the keyblade saw this as a sign of terrible things to come. So he ordered his three apprentices (Terra, Ven and Aqua) to seek out Xehanort and his cohort.
Both Ven and Master Xehanort have connections to preexisting characters. Ven happens to bare a striking resemblance to Roxas. Master Xehanort shares the same name and clothing to the other Xehanort seen in Kingdom Hearts. As you play through the story, their connections will be revealed. However, you will have to play all three scenarios to understand the story completely. The secret movie shown at the end of Kingdom Hearts II: Final Mix+ is actually a scene from the game.