Swaption (Swap Option)
  
See: Swap.
It's just the option to swap.
"I have a bond paying 8% that comes due in 2 years. You have a bond that pays 7% coming due in 8 years. Let's swap interest payments and do something fancy with the principal, and have a little cash be exchanged today to make us both feel equally crappy about the deal."
Why would we do this? Well, the bonds pay their interest in different currencies. So all kinds of needs then come into play when, say, Company A needs to fund daily operations in Zimbabwean dollars, and Company B needs Vietnamese dong.
Yes, we love dong.