It is a radio, actually. It consists of two parts: a transmitter, with a microphone and usually an audio in port, and receivers that are either integrated into the hearing aid or plug into the bottom of it.
The most common use, I believe, is in the classroom; the teacher or professor wears the microphone - either on a lanyard or as a lavalier mic, depending on the brand - and it improves the signal/noise ratio for the student. However, they're also commonly used in other situations.
Most of them let you plug in a regular headphone cable to them as an input - so I can plug in my iPod, for instance, and leave the whole thing in my backpack, which is kind of a nice bonus. A few of the lecture halls I have class in even allow me to plug my transmitter into them, so I get sound directly from the hall's sound system. One FM system - the Phonak Soundlink - even does Bluetooth, so you can interface it with your cell phone (that is, an FM signal from the hearing aid to the Smartlink, and a BT connection between the Smartlink and the cell phone).
I love my FM system, can you tell? ;-)