Old as photography itself is this question, and whilst its a repeat its often nice to get a fresh start and have new people give their insight and also for us who have seen it before to give it another rethink.
Myself I knew what I liked in seeing photography, but it was always something reserved for the richer, the smarter and those who knew the secret ways of the mystical darkroom with its demonic red lights. Then oneday I found myself with money in my pocket and not much to do and felt that I needed a new outlet for myself. I'd never been able to draw and never learned to paint or such so I thought why not a camera. By that time digital had taken over which encouraged me - I don't understand the darkroom but I understand computers (a little at least).
So I started it just with the low aim to learn the hobby; get a half nice 70-300mm ish lens and give it a go. Then something clicked - I started to understand the hobby, but also produce an end product that I was proud to have taken - and the more I worked at it the better and better that end product became.
So in part its because I could see what I knew I liked (wildlife - the BBC style stuff) but also because I enjoyed the challenge - the fact that it was the first true outdoors hobby I'd indulged in - the fact that I could (with effort) produce something that I thought I'd never be able to do.
Thus I guess part of why I do it is because I consider it something that I can be good at - I can achieve something that I am proud of (which should never be taken as me saying that I am perfect, I am always humbled by the works that those newer and more experienced than myself are able to create with both lesser and greater gear). However there is also the other side to my photography which is the outdoors part; the wildlife, insects, landscapes - in essence the ability to capture a moment of that wild beauty. I can't do it on paper with a pen or brush from the mind so I try to copy a little from reality with the camera (and sometimes use the camera to create something new)