Joe is a Looper. Looper's are time travel hit men for the Mob. In the future Time Travel is illegal so naturally the Mob has control over it. In 2072, when the Mob wants to get rid of someone they send them 30 years in the past to get “taken care of” by a Looper. Since organized crime syndicate's don't like loose ends they created a retirement package for Looper's to where your older self is sent to get executed by your younger self. The Looper kills his older self, gets a huge pay off and is supposed to live an indulgent life until the day they get sent back. I should point out that these “loose end” sent back it time to get iced are all generally masked and bound with their hands tied behind their backs.
During a routine hit Joe come to “the end of his Loop” when his older self shows up unmasked and ready, willing, and able to fight for his life. So it's Young Joe vs. Old Joe as Old Joe tries to fix his future by preventing the death of his wife while Young Joe tries to “close his Loop” and finish his job before the Mob does him in.
There is a lot more to the story but saying anymore would spoil a lot of the excitement in this kick butt Time Travel tale. It delves deep into the age old question If you could go back in time to make the future better for you (always the case) or the betterment of mankind would you do it even if it meant killing someone? The concept of Time Travel will always be cool and we will always ponder the 'what if' scenario but LOOPER does a fascinating job of making us realize how selfish and messed up Time Travel can be.