Music Packs are a feature that allow players to have custom contextual music playing in certain Biomes. You can specify tracks that will play in the Shire, tracks for Gondor, Mordor, and everywhere else. You can also add menu music. Music Packs were added in Public Beta 30.
It's a zip-file, with folders and sound files inside. In this way they are similar to resource packs; however, instead of replacing the game's tracks, music packs are a way to add your own.
The most important part of the music pack, however, is the "music.json" file. This is a JSON file (like those used in resource packs, and loads of other stuff) wherein you will define the tracks, the regions they play in, and other properties.
There is also a forum board dedicated to the creation and discussion of Music Packs.
Installing Music Packs
To install a music pack, all you have to do is to drag and drop the zip file into the folder "lotrmusic" within the .minecraft folder.
Creating Music Packs
The first step is to gather all your music and convert it to .ogg format. That's easy enough (though it may take some time!) Also, their filenames can only contain standard ASCII characters. That means none of these: á ñ ö 音 ы ق 음 ... and so on.
Then, you have to create the music.json file. This should be easy enough if you know how to format JSON. Alternatively, you can use the Music Pack Creator.
Music Pack Creator
Music Pack Creator is a program created by The Ranger Malvegil which greatly simplifies the process of creating music packs, with a friendly interface and all the necessary features! If you don't want to deal with JSON files, that program is highly recommended.
The music.json file
The file is structured as a list of music tracks. Each track has a "filename" (the name of the file), "title" (the display name, which can include non-standard ASCII) and a list of "authors". That's the basic stuff. In addition, for each track you have a list of "regions" in which it can play (roughly corresponding to larger biome groups, and the main menu).
You can then go further if you wish and specify "subregions" for each region (e.g. the fiefdoms of Gondor, specific regions of Eriador), "categories" (currently "day", "night", and "cave"), and "weight" (to make some tracks more likely to play than others) - however, these are all optional. Here is a readme file with more detailed instructions, describing how the music.json is structured, and listing all the regions.
And here is an example music.json file.
This website is quite useful: you can use it to check valid JSON.
Once that's done, you put all the tracks in a folder "lotrmusic" within a folder "assets", take the "assets" folder and the music.json, and add them to a zip file.
Music packs were initially announced using this riddle, posted on the Facebook Mod Page.