Many retrocomputers from the late 80s and early 90s had audio DAC hardware support. This includes the Amiga, Classic Macintosh, and PC's with SoundBlaster add-on cards. Despite the fact that the MP3 codec is designed to perform well at pretty low bit rates (<128 Kbps), these retrocomputers can't handle MP3 playback.
Below is an excerpt from the AmigaAMP System Requirements.
Basically AmigaAMP runs fine on any stock Amiga with at least a 68030-50 MHz processor. However, if you want to be able to play MP3 without downsampling and quality loss you need at least a 68060-50. Be prepared to face heavy system load! :-) If you've got a PowerPC you can play MP3 streams in the background without noticeable system slowdown at all.
What is the critical bit of computational capability that is so lacking in the earlier machines that makes MP3 playback infeasible?