Writing is a medium of expression, but it is more than that. Writing is a medium that allows you to relay a whole world to other people.
Crazy Ideas!
Sometimes you have crazy ideas. Sometimes it is fiction, other times it is pure fantasy. Regardless, it is something that can require pages upon pages to fully express. Think of worlds like that of Harry Potter. Only in writing can you express something like that and have the reader fully feel the essence of what you are trying to express.
Linguistics!
Language has been developed over the course of human history. There are many subtle tools that can be applied to alter your writing. It is really cool to play around with those tools to create a certain atmosphere. Whether it's dialogue, analogy or perspective shifts, all tools have a very specific purpose and a place to be used. It is really fun to play around with these and see how that affects the story you are trying to tell.
Self-exploration
Writing is more than just telling people your ideas. It can also be used to explore your own ideas and delve deeper. I find that although I can have a general plot, as I write more, I find more layers to that very plot. There are also things that happen within your own plot that can cause you to delve deeper into a topic and discover yourself further.
FUN
Sharing your writing, as well as appreciating other people's writing is just fun. At the end of the day, one of the main purposes in life is to enjoy yourself. Writing is an activity that I genuinely enjoy.