Immediate annuities (sometimes called income or payout annuities), are pretty straightforward - basically a mirror image of a life insurance policy. Instead of paying regular premiums to an insurer that makes a lump-sum payment upon your death, with an annuity you give the insurer a lump sum of cash in return for regular income payments until you die. (Actually, you have several options, including payments for a specified period of time - say, 10 or 20 years - or payments that will continue for as long as you or your spouse is alive.)
As the name suggests, immediate annuities start paying out right away, so they're are frequently used by people already in retirement. A deferred annuity can also be converted into an immediate annuity.