Cosplay is the activity of dressing up as a character from your favorite show/film/game/comic/nightmarish hallucination. Results range anywhere from 'so impressive it's almost not embarrassing' to 'worst Halloween costume in the trailer park.'
The term Cosplay comes from the words Costume Play, and takes the expression of fan-devotion to the level of self-sacrifice. In the Cosplay community, one way to distinguish yourself is to dress up as a character people only barely remember. For example, a sci-fi convention is bound to have a selection of people dressing up as their favorite characters from Star Wars, Star Trek, Battlestar Galactica. Dressing up as a more obscure character can be a good way to ensure people remember your act of elaborate self-esteem self-immolation.
This Buddy Christ Costume illustrates both the self-sacrifice and obscure character phenomena nicely.
In addition to paying homage to roles that you found interesting, Cosplay can be used to communicate which roles you personally favor over other characters. Why argue over who was the better captain on Star Trek when you can let your geek flag fly high by dressing up as Janeway?
Yes, there is such a thing as Nazi Cosplay, it's called Nazi Chic and is considered "cool" in East Asia.
Cosplay is occasionally used to give geeks literal boners, which is almost always a terrible thing for all involved.
We will not be contributing to the unrealistic expectations of our geekier readers.