This answer is provided mostly to answer your question "what is it?"
A variable annuity is a contract between you and an insurance company. The insurance company takes a bunch of money up front as a lump sum, and will pay you some money yearly - like earning interest. (In this case, they will probably be paying you the money into the account itself).
How much they return is, as the name suggests, variable. It can be anything, depending on what the contract says. Mostly, there will be some formula based on the stock market - frequently, the performance of the Standard & Poors 500 Index. There will typically be some minimum returns and maximum returns - if the stock market tanks, your annuity will not lose a ton of value, but if the stock market goes up a lot in one year (as it frequently does), you will not gain a lot of value either.
If you are going to be in the market for a long amount of time (decades, e.g. "a few years out of college" and then a little), it makes a lot more sense to invest in the stock market directly. This is essentially what the insurance company is going to do, except you can cut out the middleman. You can get a lot more money that way. You are essentially paying the insurance company to take on some stock market risk for you - you are buying some safety. Buying safety like this is expensive.
Variable annuities are the right investment for a few people in a few circumstances - mostly, if you're near retirement, it's one way to have an option for a "safe" investment, for a portion (but not all) of your portfolio. Maybe. Depending on the specifics, a lot. If you are under, like, 50 or so? Almost certainly a terrible investment which will gradually waste your money (by not growing it as fast as it deserves to be grown).
Since you want to transfer it to Vanguard, you can probably call Vanguard, ask to open a Roth IRA, and request assistance rolling it over from the place it is held now. There should be no legal restrictions or tax consequences from transferring the money from one Roth IRA account to another.