Sam's supernatural abilities are the result of him being fed Azazel's demon blood while he was an infant. Sam exhibits signs of precognition throughout the first season, manifesting as dreams of others' deaths and later as visions.

Why did Sam have premonitions?

Premonitions/Visions

Sam's premonitions began "about six months" before Jessica's death. ... Sam and Dean theorize that Sam only has premonitions when they are somehow related to the Yellow-Eyed Demon.

Why is Sam Lucifer's true vessel?

Now knowing his destiny, Sam decides to join up with Dean again to prevent it in The End. In Changing Channels, it was revealed by Gabriel that Sam is Lucifer's vessel because his relationship with his father mirrors that of Lucifer and God's.