It can means a few different things for an MP3:
[li]A totally unplayable file where no part of the song is playable. This was quite common during the time FTP was a popular way of sharing music and an incorrectly set up FTP server/client caused the songs to be transferred in ASCII mode, resulting in unplayable songs (somethings known as a ‘cooked’ MP3.)[/li][li]An incomplete song.[/li][li]Damaged headers, but where the rest is playable (like chef mentioned).[/li][li]An MP3 created by an anti-piracy organisation, e.g. a clip of a song repeated in a loop (also known as a fake MP3.)[/li][li]In some cases, a corrupt MP3 could mean a badly ripped song, where the CD was skipping.[/li][/ol]
For #1, this type of corrupt MP3 can be easily fixed by a utility called uncook95.
For #2, usually you can tell by the file size. Most MP3s of 128+kbps are roughly the size in Megabytes as minutes (e.g. ~3MB for a 3 minute song) or 50% larger for a 192kbps song (e.g. ~4.5MB for a 3 minute song). If you see an unusually short file, especially <1MB, then it’s mostly a truncated song.
For #3, just open it in any playback software. If it refuses to play or shows garbage info in the song details, then it has a corrupt header.
For #4 & #5, the best way is to play the full song. While some software can claim to detect fake songs, there is always a risk of a false positive or missing bad sections like CD skipping/glitches.
Of course the only sure way of checking if an MP3 is corrupt is to play it. If it plays fine from start to finish, well then it’s most likely ok.