LIBOR-in-Arrears Swap
  
If you are dating a person named Libor, you might not want to tell them about this one. He might get the wrong idea.
This transaction is a form of credit swap, so we'll start with the basics there. A credit swap typically involves trading the proceeds of a fixed-rate debt security with the proceeds from a floating-rate one.
The owner of a fixed-rate bond wants a little more action; they want the potential upside of an investment that can move along with interest rates. Meanwhile, on the floating-rate side, they are looking for more stability. They like the idea of knowing for sure what the return will be over the long haul.
So the two sides make a trade. They don't trade the actual holdings. They just trade the money generated from the investments.
Usually, the floating-rate part of this transaction is set at the beginning of the swap period. The LIBOR-in-Arrears version changes the timing of this. The rate gets set at the end of the period instead. Then the rate, once it's set, gets applied retroactively to the time period.