People carried around all their favorite CDs in a giant CD case.
If you wanted to be the DJ at your friend's birthday party, instead of making a playlist, you'd have three choices: 1) to bring all of your CDs over, 2) to burn a CD, or 3) to make a mixtape. None were as easy as just hopping on Spotify and compiling your favorites.
Even just listening to music on your discman involved carrying these cases around, unless you wanted to listen to the same 15 songs on repeat.