If you have music files on the ipad itself, you can airplay them directly using the ipad's music app. If you have these music files only on the ipad and want to use the remote app, then you will have to first download them into your itunes library on your computer. Make sure in itunes under the "music" submenu for your ipad device that you have "sync music" enabled - I think it's turned off by default. You can choose to sync the entire library or select specific playlists, artists, albums, etc. I personally have created a playlist just for my iphone as I have a big library and not everything will fit on the iphone.
Presumably this is your problem. If the files you mention ARE in your itunes library & still not playing, then there are other issues involved.