Stages are all the places you can select inside the game to fight with your opponent.
Mugen allow you to add or remove all the stages you want.
The variety of stages on Internet is really good, from videogames like King of Fighters, Samurai Shodown and Mortal Kombat or original works designed by talented people.
Some Stages have amazing images with animations and colors.
HCM has a special section to download Stages.