playlists are held in the android media database. This lives in /data/data/com.android.providers.media/databases.
If your phone is not rooted, you will not see any files or folders here. Depending on the format of playlist backup, all you need to do is place any playlists in the Playlist folder (or any suitable folder) Android Media scanning will pick them up and automatically import them into the android database. Suitable format are playlists with .m3u extensions.