DirectMusic is a high-level set of objects, built on top of DirectSound, that allow you to play sound and music without needing to get quite as low-level as DirectSound. There is strong support for dynamic soundtracks - having music which changes in response to events in the game.
DirectMusic is part of the DirectX library and was introduced in February 1999 as part of the 6.1 version of the library.
DirectSound and DirectMusic have had a fairly radical overhaul since last year, and the two APIs are now much more closely linked, making it easier for developers to apply DirectSound effects to DirectMusic, or to use DirectMusic to create dynamic sound effects.
DirectMusic can then switch between these depending on the player's actions, changing at the end of a beat or section of music, and playing transitions as necessary.
Microsoft are particularly pushing DirectMusic as a solution for sound and music on their X-Box console, and with DirectX 8 they are trying to make it easier for developers to use dynamic music and sound effects in their games, and to apply a variety of audio effects to them.
DirectMusic: for playback of soundtracks authored in DirectMusic Producer
DirectPlay is deprecated in favor of Xbox Live whereas DirectShow will be deprecated in favor of Media Foundation, a different set of APIs debuting with Windows Vista to handle audio and video playback.
DirectMusic will probably remain the only component intact.