if you use the iTunes Get Album Artwork feature, it does not embed in the file, as you apparently noticed. If you want the file embedded in the file, find the artwork on the Web. Right-click the track in iTunes, Get Info, and paste it into the Artwork tab, then OK.
Also, if you use Get Info to change Artist, Album ,Year, etc, the info will get written to the file when you OK out, and thus will be there when you play the file elsewhere.