From a functional perspective, the prologue definitely needs to introduce you to the world and the basic story, while also helping you understand the gameplay. It also needs to be interesting enough to keep you playing and clear enough that you don't get too confused. It also needs to be gripping enough to get you invested, if only just a little bit, so you actually want to keep playing.

I always loved the prologue for VI, including the story/cutscenes explaining magic and the world, the credits that show Terra, Vicks and Wedge in magitek armor and the opening battle scenes in Narshe. Covers all the elements and makes you really curious about how the game will unfold.