It doesn't matter how many times I read that it just never makes any sense to me. Why send them back in time? Why not just kill them? How is that any better? What am I not getting here?
The film explains that it is much harder to dispose of a body in the future due to "tagging techniques and what not". So the mob sends their target back 30 years to a Looper, hog tied and with a sack over their head, to be killed and disposed of.
The time machine is set to a fixed time of 30 years to the past, wich explains why they wouldn't just send them back to the dark ages or something. Though that could also severely alter the future sending them back that far dead or alive anyhow.
But the whole "kill your younger self" thing would just cause a paradox, thereby undoing the murder anyway.
Unless there's something I'm missing.
The older version (Willis) is sent back to be killed by his younger self (JGL) in a process that is called "Closing your loop".
I've read the screenplay and seen this at a screening a few months back.
Hope this clears up some confusion (: