Emo can be defined in various forms. More so, people commonly will refer to it as a genre of music, but mistakingly. Take Linkin Park for example, or Three Day's Grace. They are ALTERNATIVE, but they're considered Emo Rock for a reason.
That reason is that Emo people listen to it. Emo people are those who like to cut themselves (usually) or just hate their lives. They are easily depressed and wear normally dark clothing. More-so it's just a form of depression and in some cases, bi-polar disorder. But that's aside the point.
Emo can be defined how you see it. Emo can be someone who's overly happy, a person who is very moody, or someone who's always one specific mood -take depression for example, so that proves my point. But the common Emo is the one I stated before now.
If you ARE a cutter Emo, please seek help, it's not good for you or anybody else's health. Talk to somebody -a friend, a parent, a teacher, someone who will listen- to get advice on your life and decide if it's really that horrible.
But overall, there isn't much a TRUE definition for the word "emo". It's all about how you percieve it, so don't get too confused. And when I say that, I'm referring to modern times, not anything else that's happened in the past.
My examples are a little extreme; don't take them too literally. And don't try to change yourself to be an Emo in any form just because you want to be like somebody else. You'll only appear like a poser, so just be who you are.
An example of a depressed emo-
Emo Kid: My life is a wreck. I wish it would just go away.
Normal Kid: Aww, don't be that way, cheer up a little!
An example of Emo Rock (Songs with depressing lyrics)-
Linkin Park, Three Day's Grace, (sometimes) Nickelback (thought not all the time so don't get mad because I personify it this way ;) ), and sometimes Green Day. Though most of these bands are described as Alternative/Metal. Once more, all about perception.
An example of moody person (another Emo form)-
Moody Kid: I want to kill myself now.
Moody Kid: I don't know, let's go play soccor! *Moody kid smiles*