Annuities are a pretty polarizing topic... I believe that financial products are like tools: Every tool has a purpose, and when used for it's intended purpose, it works great, but problems arise when someone tries to use a hammer for everything!
Buffered annuities are a relatively new financial tool designed to provide modest protection from loss, balanced with plenty of opportunity for gain.
Some products, like the popular Shield series by Brighthouse Financial, manage to accomplish this with 0 fees. Which a lot of people like.
The diagram below gives an idea how they can work. Essentially, you choose an investment (or index in this case) and your returns are based on the performance of that investment over a period of time, say 3 years. The insurance company will protect ("buffer") you from a percentage of loss, and in exchange, put a limit ("cap") on your maximum gain.
If the investment goes down more than the percentage, you lose the excess. If it goes up more than the maximum, the insurance company makes the excess.
These products make sense for people who don't want to risk it all in the market, but want better returns than you can get from more conservative products like CD's and fixed annuities.