A Grammar Nazi can be defined as one who compulsively corrects grammar mistakes. To most of the internet, they seem a nuisance. However, in some cases, they have actually taught people more about grammar than their L.A. teachers.
A Grammar Nazi could be anyone. It could be your standard nerd, to your standard sports player. One thing to note, however, is that they are likely to be more on the nerd side (not necessarily, but generally) and are picked on and/or physically harmed due to their superior knowledge on grammar.
The average Grammar Nazi will immediately correct any given grammar error. This isn't very easily avoided, so it is suggested that anyone who knows a Grammar Nazi have at least a decent amount of patience.