Annuities are the opposite of life insurance in that they stop paying a benefit at death.  The way annuities work is that a company (often an insurance company) will take a lump sum of money and pay it out in installments until death.  Annuities protect against financial loss from living too long, while life insurance protects against financial loss from dying too soon. 

Why would someone want to do this?   Well, since people are living longer, there is a danger of living longer than your retirement savings can provide.  An annuity keeps on paying, so the annuitant (person receiving payments) has a guaranteed source of income, and doesn't need to fear running out of money.

Why would a company want to do this?   The catch is the company stops paying when the annuitant dies, and keeps any money left over. 

Now if that doesn't appeal to you at all, you can choose a common annuity option which will continue paying income to a secondary annuitant (spouse or kids).  Or you can set up the annuity to pay for a specified number of years.   Since these methods reduce the chances that  the insurance company will make a big profit, the monthly income payments will be less than if it were a standard annuity.

Insurance companies are big into annuities because mortality estimates are how a company determines how much income to pay out.  The longer an annuitant may live, the smaller the payments would be.