Inverse or bear market ETFs are designed to do the opposite of whatever index they track. For example, DOG does the opposite of the Dow Jones Industrial Average (DJIA). If the DJIA goes up 1%, DOG goes down about 1%; the DJIA goes down 2%, DOG goes up 2%.
You can use inverse ETFs to make money when the market goes down, whether to hedge your portfolio or just to bet that the market will go down over a certain period, without having to short sell anything.
I wrote this previously: "You should remember that inverse ETFs go down when the market goes up, and the leveraged ones go down twice as much. As over the long term the market tends to go up, it's probably best to use inverse ETFs to hedge your loses in rough times or for short term gains."
To emphasize, I'd like to add that if you use inverse ETFs, you have to pay attention to them. Holding inverse ETFs too long will always lose you money. (Well, not always. It is always possible for the market to go down over an extended period. But if this happens, there will probably be other things to worry about than the stock market.)
Here's a case in point. Some time ago, I created a Motley Fool Caps account. You select stocks, and say whether they'll outperform or underperform the S&P 500. Your picks are tracked, and you're given points. At the time, I thought the market was going down. So, I loaded up on inverse ETFs, and leveraged inverse ETFs (they do double the opposite direction of the index they track).
As you can see from the chart, I did really well between March and April of 2008. Then, this not being real money, I completely forgot about it. By May 2008, I was down almost twice as much as I had gained.
The lesson here is, if you use inverse ETFs, it has to be for the short term, and you have to watch them like a hawk.