All annuities are a form of an agreement with an insurance company. You give the insurance company your money to manage, and in return they provide you with a policy, which spells out the benefits they are providing to you.
There are two main types of annuities; either immediate or deferred. Immediate annuities come in the form of a fixed, variable or inflation-indexed annuity. Deferred annuities come in the form of a fixed, variable, equity-indexed, or longevity annuity.
Each type of annuity functions differently, and may or may not be an appropriate investment for you, depending on your personal circumstances.
Immediate annuities provide a guaranteed stream of income to you. You purchase this stream of income by giving the insurance company a lump sum of money; in return they calculate how much monthly income they can provide to you based on the type of annuity (fixed, variable or inflation-indexed) and based on the term of the annuity that you choose (life-only, joint life, term certain).
With deferred annuities, you deposit your funds with the annuity company (by investing in either a fixed, variable, longevity, or equity indexed annuity) and the taxes on any investment gains are deferred until such time as you take a withdrawal. Written into your deferred annuity contract will be the option to turn your deferred annuity into an immediate annuity after a certain amount of time has passed; essentially you are letting your earnings defer until such time as you desire to turn the investment into a guaranteed stream of income. Deferred annuities can come with all sorts of features (at a cost) that provide specific types of death benefits and/or future income guarantees.