Generative art is all what Shadertoy is about. I think this video explains quite well what it is. Tim Holman - Generative Art Speedrun

As this Three.js page explains very well, you will not here develop a full 3D application, but short GLSL programs for fun or to experiment and learn about 3D rendering technics.

I can see shaders in the following main categories (personal point of view)

• Masterpieces
  • Here the creator tries to sum of many different technics in the same shader. Need weeks of work. The creator wants to prove and show his artistic and technical skills.
• Nice Illustrations of functions and algorithms
  • Tutorial, here the creator wants to make a visualisation of what he learnt and wants to communicate, like construction of polyhedrons or the rendering of clouds.
• Reproduction
  • The author tries to reproduce a picture, or a scene of a movie for example, for the pleasure.
• Golfing
  • Making very short program, the pleasure is to find how its works with so few characters !
• VJing (Video Jockey)
  • Some shaders like spychedelic fractals may be used during “parties”.
• Results of live coding parties.
  • Memorize some formulas and retype them quickly, you will impress your audience.
• Playable games and emulators
  • No idea how they can even do it !
• Optical illusions
  • Fun ! But be prepared for headhatches if you look at it too long.