Emo

Originally short for emotive hardcore, a subgenre of hardcore punk and post hardcore catagorized by more personal, emotional, and confessional lyrics. It is not a shitty subculture of edgy teenagers who are desperately trying to be unique and different, those are just scene kids. No, chances are if you see it on a shirt at Hot Topic, it is not an emo band (Or a screamo band for that matter).

Some examples of emotive hardcore bands are:
Embrace,
Rites of Spring,
Moss Icon,
Indian Summer,
Dag Nasty

Emo more commonly also refers to another genre known as midwest emo, indie emo, or simply just emo. This type of emo is more closely related to indie rock (which is also probably different than what youre thinking).

Examples of indie emo bands
are:
Sunny Day Real Estate,
Cap'n Jazz,
Joan of Arc,
Jimmy Eat World (early),
Mineral

Both of these types of emo often include shouted, screamed, or occasionally sloppy vocals, respectively.

Respectable emo fan: "Moss Icon is a really good and influencial early emo band."

Scene kid: "i luv emo!!!!1 are they like My Chemical Romance??? RAWR XDDD"

Respectable emo fan: "God has abandoned us."