1
What it actually is
A swaption is an option to enter into an interest rate swap on pre-agreed terms — fixed rate, notional, tenor — at a future date. Buy a "payer" swaption and you get the right to pay fixed; buy a "receiver" swaption and you get the right to receive fixed.
Like any option, you pay a premium today for that right, and the terms of the underlying swap are locked in from the start.
2
Why someone would do this
A company expecting to take out floating-rate debt in six months, but worried rates will have risen by then, can buy a payer swaption now.
If rates do rise, it exercises into a swap at the old, better fixed rate; if rates fall, it lets the swaption expire and takes the better market rate instead. It's optional protection on a rate decision that hasn't happened yet.
3
Who's actually doing this
Corporates hedging anticipated future borrowing, and banks managing the optionality embedded in things like mortgages — where a borrower can prepay, which behaves like an option the bank is short.
The exercise style usually mirrors how the real-world decision actually gets made: a single moment, any time, or a handful of fixed dates.