Determine if the phone supports cover art image files and the right filename and format
If you're using the Google Play Music app (which is the stock music player in many phones, and is available for phones running Android 2.2 up if not) to play your music then this Google Support article "Copy music files directly from your computer" says:


  If your music files have accompanying artwork in .jpeg format, rename
  the art file albumart.jpg and include it in the same folder as your
  music files.