Read the fine print because I guarantee they have never "bought a clients home." The whole thing comes down to pricing your home correctly. Sometimes that hurts when a seller was expecting their house to sell for a certain amount and the market has turned against them.
People using catch phrases like that are often just trying to lure you in. They will attract leads and convert some. Your Realtor or Agent needs to be in your corner and represent your best interests. Make sure they are doing that by asking a lot of questions and even interview several of them to make sure you feel comfortable with them and how they plan to market your home.
Price you home correctly and show it in it's best possible condition and it will sell before its competition for the best possible price. That is a Guarantee that I stand by with my clients.
Best of luck to you.
The main string is the preset price reductions that Teddy mentions. Example (this doesn't relate to the specific program you're seeing, but in general this is how it can work): Let's say your home is worth around $400,000. The arrangement might be to begin the listing at $400,000, and to drop the price by $20,000 every 3 weeks down to a floor of $260,000. If it hasn't sold by that time (that'd be 21 weeks), they'll buy it. They're figuring that it should certainly sell before that point--at least around $360,000 or so. And they're figuring that if it goes all the way down to $260,000, they can buy it and resell it for more almost risk free. If the property really is worth $400,000, they can buy at $260,000 and sell at $350,000 or so. (They'd better figure out why it didn't sell at $260,000, though!)
I've also heard of some agents getting into trouble with such programs--they've ended up owning a couple of homes that were apparently worth far less than they'd thought.
If I were a seller, I'd personally rather have the flexibility to adjust the price based on market conditions, number of showings, number of offers, and so on. On the other hand, some sellers do like the promise that the home will be sold, one way or another.
So: Talk to the local agent, if you wish. Get the details of the program. Determine your comfort level with it, and whether you can live with the process and the numbers being proposed.
Hope that helps.