An annuity is a product that is sold by financial institutions to investors. The investors pay in a certain amount of money over a period of time, and then at a given time (called annuitization), the annuity starts to pay out money to the investor for a given period of time.
The firm using the annuities uses the money investors pay in to grow the funds in order to pay for the cash payments in the future. This is similar to a mutual fund, except that the returns are guaranteed.
Investors wishing to set aside money for their retirement frequently use annuities. The individual investor is assuming they will live long enough for the annuity to pay more than they invested whereas the firm is betting on the fact that the investor will claim less than they paid in.