To grossly oversimplify, it's like a walkman.  Well, a portable MP3
player would be like a walkman; they don't have to be portable.  They
make them for your home stereo, your computer, or even your dashboard.

MP3 is a file format (same idea as an MPEG or quicktime MOV) which
compresses roughly one minute of at-least-CD-quality music into one
megabyte.  Which is to say, that you can take all the music on a CD and
save it to your computer in a file 1/10th the size.  Now a megabyte used
to be a lot (believe me I know, I learned to program on a TRS-80 with
cassette storage) but with hard drives so cheap now, you can literally
fit every piece of music you have ever owned (heard?) onto a $1000
jukebox, err: computer.  I have about 4 hours of MP3s on my mobile
phone, which I use as a walkman when I'm snowboarding or sailing; you
have to hook the phone up to the computer to get new songs loaded up,
but it's worth it.

Isaac in Cambridge

ps.  This technology, which has been around for years and years, became
very popular recently when some clever kid from Massachusetts figured a
way to let people share their record collections (in MP3 form) over the
internet.  This was called Napster, and made the recording industry blow
smoke out their ears.