With an Immediate Annuity, your income payments start right away (technically, anytime within 12 months of purchase). You choose whether you want income guaranteed for a specific number of years or for your lifetime and/or jointly with a spouse. The insurance company calculates the amount of each income payment based on your purchase amount and your life expectancy.
A Deferred Annuity has two phases: the accumulation phase, where you let your money grow for a while, and the payout phase. During accumulation, your money grows tax-deferred until you take it out, either as a lump sum or as a series of payments. You decide when to take income from your annuity and therefore, when to pay the taxes. Gaining increased control over your taxes is one of the key benefits of annuities. They usually have charges if more than 10% is withdrawn for the first 4-7 years. Each annuity can greatly vary with its own rules.
A Fixed Annuity generally guarantees a certain interest rate through the accumulation phase. It is chosen for its perceived safety and assurances. Similar to a Certificate of Deposit (CD), there is no volatility of principal.
A Variable Annuity is the most popular type of annuity. They allow you to invest premiums in a limited number of subaccounts, which are mutual fund-like investments bundled in an "insurance wrapper."
Equity-indexed annuities (EIAs), also called fixed-indexed annuities (FIAs), or more simply "indexed annuities" are similar to fixed annuities. They offer minimum and maximum interest rates that are based on stock market index returns. As such, the principal isn't subject to volatility, but it still has some growth potential.