Cocoon's government is using crystals with the power to change man's destiny to force those on Pulse to work against their will. In turn, the citizens of Pulse are rebelling. Their force is led by the only confirmed character so far, a feisty woman who goes by the codename of 'Lightning'.
Apparently the player won't know if he's (Note: I presume by "he" they are talking about Mr. 33cm) on Lightning's side or not until a certain point in the game. One new feature to help develop the story will be a 'split-screen' of sorts, showing different characters in different locations on screen at the same time."
Basically, Lightning is heading up a rebellion fueled by the people of Pulse and the poor treatment they've gotten from the Government of Cocoon. As for the split screen, this will probably be for cut scenes as having a window to other characters on your screen while in battle or running around doesn't particularly make much sense.