Typically it means to play a song so much that your interest in it degrades, but
the word's meaning is not limited to just music.
Almost anything that you can "play" can become less interesting if you do it too much. Video games, sports, etc.
Unless you have a strong passion for something, then you normally can do it as much as you can and your interest in it will never
decay. For example, gamers that somehow main the same game for years.
A very similar word is overuse.
Example 1: (Just imagine any song playing in a car) I mean this is a good song, but it's slightly annoying now because my favourite radio station overplays it. It's like every 5 minutes they play this goddamn song.
Example 2: I used to love
Carpenter Brut to a point where I couldn't stop listening to their music. But i
overplayed their songs so they're not as enjoyable as I remember.