Amiga was a popular home computer in 1980s and early 1990s. Demos are programs that generate multimedia presentations in real-time while demo is running. This separates demos from animations that are not limited with this real-time constraint.
In Amiga 4k intro competition these programs are limited in size to 4096 bytes. 4096 bytes is comparable to the amount of text on one A4 sized page and therefore takes real skill to fit great effects and music to that size.