On the surface, a femtocell, also called a "microcell" (AT&T) or "network extender" (Verizon), sounds similar to a booster. You stick it in your house and it broadcasts a strong cellular signal.
The difference is that the femtocell needs to plug into your router so it can use your internet connection. That's how it connects your phone to the carrier's servers.
The upside is that a femtocell will work in an area where you have absolutely no signal at all. So it's good for rural locations or an apartment surrounded by high-rise buildings. Just note that it doesn't work well with satellite internet.
The downside is that if you get one of these from a carrier it will only work for that carrier's phones. And in this case, third-party options that cover multiple carriers are practically non-existent.
Plus, anyone who uses that carrier can also use your signal, even if they're strangers just walking by. Their calls will go through your internet connection, possibly slowing down your own traffic like streaming movies or other downloads. With Verizon, you can set priority numbers so you always get service first, but other people could still be leeching off your internet connection.
Many times your mobile provider will loan you a femtocell for free or for a one-time fee. It's better for the carrier to provide a femtocell for free than to lose a customer.
If your carrier doesn't loan it to you for free, femtocells will set you back anywhere from $50 to $250, depending on the brand and the amount of data. Fortunately, there's another option that's about to make them obsolete.