An FM transmitter allows a music phone to broadcast music on FM frequencies at low power, so that the music can be heard via nearby FM radios.
This is most useful for using your music phone with a car sound system. It can also be used with a home system, or to allow a group of headphone-wearing friends to listen to the same music simultaneously.
The sound is transmitted wirelessly, like any FM broadcast. The range is very short, though, as required by law, so it does not interfere with FM radio stations for your neighbors, etc. In many cases the short range can limit the effectiveness of this technology, even in spaces as small as a vehicle interior.
Most phones with an FM transmitter allow you to choose the frequency, so you can choose one with the least interference.