I see a few reasons why people do it:

1) They feel that for whatever reason, the world hates them or they hate themselves or someone else hates them, however, they don't want to go and actually commit suicide because something is holding them back. Perhaps it's love for someone else, fear, etc... .
2) They want attention in the form of help for whatever the issues are that they're having but they're lacking confidence or something else is holding them back from getting help. Perhaps they think they have nobody around them who they could talk to. So, the cutting is somewhat like a sign for others, however, they also tend to realize that it's something frowned on by society and abnormal, sometimes they may even be ashamed of it so they cover it up.
3) They've hurt themselves in some way and as we can all probably testify to, endorphins, enkalphins and other biochemicals are secreted that ease the pain, and to an extent, they can sometimes even make it pleasurable. However, the feeling does not last and so once it's gone, the only way to get it back is to harm again, again and again. I know it may sound somewhat odd, however, to save writing a ridiculously long post about the neurophysiological and neurochemicals involved in all this, I'll just leave it at here.

All of the above reasons are assuming that there's some thought or cognitive processes that's driving them to continue with and initiate the cutting. However, another reason, outside the realm of the premise I described above, is attention or even humour when people may find it funny to do so and so they do it to mock someone else. However, it's humans nature, that when we see someone who is injured, regardless if it's self-inflicted or not, we tend to want to help. When we see that the person is so miserable or addicted to self-inflicting damage onto themselves, we can easily figure out something isn't right with them and that it's a red flag for them requiring some intervention.

Lastly, look around in the media. You see a plethora of things but you'll also notice something, specifically with music, that pain, suicide, etc... is glorified. Some music bands have songs devoted solely to some negative emotions or suicide and what do they get as a result? A massive fan base, selling merchandise glorifying this. What this does is make it more common in society and to a point, make it more heard about and more accepted. It's still frowned upon but to a lesser degree and sadly, many people don't frown upon it, many people approve of it, such as the fan bases who cheer when their band comes on stage just to sing about how miserable life is, suicide, break-ups, etc... . People aren't sobbing about it, no, they're cheering about it. Strange world we live in.