There's this world called Pulse, inhabited by the fal'Cie. Now, the fal'Cie are crystal supernatural beings with great powers [e.g. Anima]. There they made a group called Cocoon fal'Cie which made a paradise that floats on the surface of Pulse, called the City of Cocoon. Most of the citizens of Cocoon hasn't even seen what Pulse is. All they know is that Pulse is a very dangerous place, and anyone who makes contact with anything related to Pulse would be "purged" (be quarantined and exiled) to Pulse.

The fal'Cie has the ability to brand people the power of the crystals and send them on special missions, called Focus. The people sent on this mission are called the l'Cie. Failure to do the focus makes an l'Cie become a ghoul called Cie'th, this also happens when your time to complete the focus runs out. Completing the focus turns the l'Cie into a crystal and is said to given eternal life.

:) That's all I got for now. Can't wait to go further into the game.