Lol. Emo, what a horrible label to use. Although I'm sure you mean well..
Emo = Someone who pretends to self harm and be angsty for attention.
Depressed Person = Has a genuine mental illness and may use self-harm as a coping mechanism.
So to call a person with a mental illness is kind of.....insulting/demeaning? Belittling their condition?
Even though you haven't known each other very long it shows that she feels comfortable and trusts you enough to tell you about it.
The reason she told you about it, is because she wants you to know. Maybe it's her roundabout way of asking for help and/or support whether consciously or subconsciously.
Do you want to help your friend? For this I applaud you. Try and educate yourself a bit on the subject.
I'm going to speak generally. Mental illness and self-harm are complex issues and I don't know you, and I don't know your friend so forgive me if I'm off the mark...
Everyone deals and goes through depression a little bit different from each other. Depression in a nutshell is when a person faces an obstacle or situation where, they just cannot cope or deal with. So they may resort to self-harm, like cutting.
People usually cut or self-harm because they have no other outlet or coping mechanism to employ. It's usually triggered by something, might be an event, something somebody said, something they thought off that made them upset~ When they self-harm, apparently there is a feeling of relief whether psychological or from the endorphins released in the brain (physiological).
This image from Wikipedia explains pretty well in an easy to understand fashion
It's good that your friend is going to therapy. Hopefully the therapist will arm your friend with the tools she needs to overcome or come to terms with her troubles. But, it's hard to go it alone. So support and encourage her where you can, and try to suggest her parents go along with her to the therapy sessions (if she's comfortable). This way the therapist, (if they're good) can give them the tools and knowledge to help her. Doesn't have to be for the whole session, can be half.
As a friend you could help her out by being there for her, being supportive and not judging. For example, if she feels the need to self-harm, maybe you can let her know that she can call you (if you're comfortable) and just talk her through the moment. Sometimes, people lose perspective and build up their problems in their head. It's like, they more they think about it, the bigger their 'problem' gets. These moments have their peaks and troughs, and they don't last forever.
Another way you can help is by sitting down together and helping her come up with a list of alternatives to self-harming. Here's an already made list
It may not be easy. Depressed people generally tend to be negative people, and sometimes they can lash out! Also you may get sucked into the vortex of their negativity. Misery LOVES company. So be aware of your own boundaries, needs and limitations.
Darn I think I wrote too much...oh well, maybe other people will stumble across this, and it'll help them out...
If you have any more questions feel free to ask~
I wish you luck.