Stereotypically speaking, an emo person is like a new "goth" form. Only they tend to dress in more colors than black and that they are popularly known to perform self-mutilation. They are also labeled as adolescents who say "I love you" a lot and talk about their problems with their EMOtions.
Seriously speaking, it's just a fad that people like to label themselves with.
ThatGirlMarz has a good answer up there, so does funnylittlefrog. basically, it's punk and goth mixed together and then taken to extremes. most of the punks tend to cut. the goths tend to wear dark colors most times. I'm kinda a mix of punk and goth, my sister sums it up in one word: vampire. mine leans more toward the goth side though.
it's short for emotional. it's basically people that have a lot of problems in their life and they decide to cut themselves to help them feel better. it's not a very glamorous life at all. I've been there