A variable annuity is an investment vehicle designed for retirement savings. You may think of it as a wrapper around an underlying investment, typically in a very restricted set of mutual funds. A variable annuity is especially attractive to a person who makes lots of money and is trying, perhaps late in the game, to save aggressively for retirement. Unlike a conventional IRA, the money you put into an annuity is not deductible from your taxes. And also unlike an IRA, you may put as much money into an annuity as you wish.
Most people are much better off in an equity index fund.
Index funds are extremely tax efficient and provide, overall, a much more favorable tax situation than an annuity. The growth of an annuity is fully taxable as income, both to you and your heirs. In plain English, the IRS treats the index fund as though your heirs just bought it at the value it had when you died. This is a major tax advantage if you care about leaving your wealth behind. Tax considerations aside, the index fund is a better investment.