It's a challenge to see who can get the most impressive visuals in a specified size of memory or other restrictions.

It dates back to when early games and software were pirated by teams. Each team would try and leave their intro video in the game as their signature, trying to one up each other.

Then it just turned into it's own form of competitive Development.

Basically you get some incredibly small amount of memory, and it's about trying to be as clever as possible to get the coolest visuals in there.

Many prominent graphics engineers were involved. Some of them even worked at studios like Pixar, making things like the vegetation systems on Brave.

The simplest explanation is that it's people making programs for the sake of it, not for any practical purpose.

And such people (as people do) tend to coagulate into a community around that interest, sharing results and techniques and overall socializing!

I'm from Brazil and wasn't even born yet at the time, but if you want to easily see a bit of what demos were, one of their "modern equivalents", so to speak, would be Shadertoy [1]. There are also videos of old demos, and I'm sure there are archives of the programs, but I haven't searched for them either.

It's a way programmers have to show off, have fun or be artistic. You write a programme but you restrict yourself in some way such as creating it for a 1980s era computer or by file size say the entire thing has to fit inside 4KB or some other extreme limit, and then you try to do things using visuals and/or music that you initially wouldn't think are possible.