A payer swaption gives the right to pay fixed, gaining if rates rise; a receiver swaption gives the right to receive fixed, gaining if rates fall. Contracts are quoted by option expiry and swap tenor, so a 1y10y payer is a one-year option on a ten-year swap.
Borrowers use payer swaptions to cap financing costs on debt they may or may not issue. Mortgage investors use them to hedge the prepayment option embedded in their holdings, which is why swaption volatility and mortgage hedging flows are linked.
Settlement can be physical, entering the actual swap, or cash, paying the swap's value. Pricing depends heavily on the volatility surface for rates, and the instrument is a primary vehicle for trading rate volatility itself.
Related: interest-rate-swap, swap, implied-volatility, dv01, forward-rate-agreement, variance-swap