The Bluetooth protocol is used to communicate between all manner of diverse types of device. In order to ensure that you don't try to do something silly like play music on your heart rate monitor, devices must declare which of the various profiles it supports. Of course it is becoming increasingly common for devices to be capable of multiple different functions and so the standard allows them to declare support for more than one profile.
The most common type of Bluetooth device, is a hands-free unit which allows you to make phone calls while driving your car without taking your hands off the wheel. These devices implement the Hands-Free Profile. These devices must be capable of outputting sound, so it should in theory be possible to use this device for listening to the music stored on your phone.
Unfortunately, many of these devices don't declare that they implement the A2DP profile. Perhaps this is because the A2DP standard states that devices implementing this profile should be capable of outputting high quality audio and many hands free units have poor quality - but high quality is a subjective judgement which should be left to the user to decide.
If you have such a device, don't panic because there is an android application called BT Mono which can solve the problem for you. It works by fooling your hands free unit into thinking there is a call in progress and then whatever sound you play on your phone will be directed to the hands-free unit.