AirMusic Free is designed to pull music from your Dropbox folders so that you can listen to it on your iPhone without having to be connected to iTunes or iTunes Match. The app, itself, works well enough, though there are numerous extra steps involved because Dropbox is not typically used as a music storage tool. That aside, if you do store music in Dropbox or if you are interested in avoiding iTunes and its pricy Match service, you can use this instead, with great effect.
After installing the app, you must set it up to access Dropbox. After approving access for your downloads folders, you can find music and start adding it to playlists in the app. Creating new playlists is easy and as you add files or download them to your device, they are automatically sorted by artists and album for easy reference. You can, in effect, create an alternate music library on your iPhone. The playback and interface are not nearly as advanced as Apple's, however, and because of space restrictions and the lack of streaming from Dropbox, you'll be limited in what you store on the device.
All of these are small issues in the end, because if you are interested in the idea of an alternative to the core tools built into iOS 6, then this works well enough for that purpose. Despite the extra work required in moving files to Dropbox, the resulting playback options are good and the tool works like many other music players on your phone, including background playback.