Final Fantasy XIII-2 (FFXIII-2) picks up three years after the events of Final Fantasy XIII. Lightning, the main protagonist of the original game is feared dead and her sister Sereh is left to fend for herself and try to find out what happened to lightning. Noel is a character from the future who was sent back to assist Sereh restore the world to its former glory and ensure a world changing event does not happen in Sereh's future. He also knows where Lightning is and so the two set off on the main adventure with different wants, but one main goal.
FFXIII-2 for the most part is very much like the original game. It's not as open world as previous Final Fantasy's, but to say that its 'on rails' would be unfair to how much effort Square Enix has put into opening the game world. There is a strong focus on time travel with each area you visit in the game set in a different period of time and as you would expect a key facet of this is being able to stop events before they occur and to try and change the path of time. This is one of FFXIII-2's successes. Seeing the world at different times of history show how the universe the game is set in changes and adapts and it offers freshness to the game that we did not see in the original title.