There is something about this question that makes my toes curl. It may be because I imagine a sleek and prosperously corporate man in a very good suit asking me the question, hand on my shoulder, condescending expression on his face. If you are such a man please don't take offence, it is the air of condescension that is at issue not the rest of it. Anyway, I digress, my toes aside, this is actually a very good question to ask yourself if you are or want to be a writer.
If I ask people why they want to write, I tend to get answers like: 'I've always written,' ' I love making up stories,' ' I don't know -they say everyone has a novel inside them.' These and all the other answers like them are fine as far as they go, but they don't go very far. They are useless in establishing what a person wants to achieve with their writing, what, in fact, their writing is for.
'Ah, but why does writing have to be for anything? Why can't it just be something creative that people do.' I hear you ask. My answer is, it doesn't have to be, but it always is.
Writing is often enormously pleasurable, it takes you somewhere else, other times, other places, but there comes a point in every piece where it gets hard. Everyone needs a reason to get through the hard bits and when you know the reason, you know what your writing is for. Those reasons are myriad. Some people write to make sense of things that have happened to them: writing as therapy can be a powerful tool for mental health. Some people write because they think their story, usually about their life and insights into it, are interesting and worth writing down for posterity. Some people have a great idea that keeps them awake at night and need to write it up, just to get a good night's sleep. There are as many 'fors' as there are people.
The 'What does success look like?' question forces writers to think one step further, to think about their writing ambitions. If you ask that question directly, you are likely to get a laugh, a shrug, an 'Oh, you know I'd be happy if just one person read it and liked it,' or ' I don't have any. You know this is just for fun. I'm writing for myself.' Women of a certain age, in particular, tend not to be up front about ambition, fearing that it makes them seem too pushy or egotistical. The 'What does success look like?' question makes the issue at once less personal and way more revealing.
'Success' might be having a life that includes more creativity in it or better understanding your own 'journey', it might be meeting new and interesting people through a writing workshop or learning to write in a more persuasive way. It may be having something tangible of yourself to leave to your family, it may be getting an agent, or getting conventionally published, or writing an award-winning best seller. It might indeed be world domination, which is good to know.
As a teacher, what I take from the other answers above is whether you are wanting to write for fun, as therapy, for a small audience of family and friends or as a professional. That's useful to me in offering support. I also know that if success looks to you, like a great deal of money, accolades and interviews on daytime TV, you need to know that writing may not be the easiest way to achieve it. Writing rarely makes you rich. No, really trust me on this, 'rarely,' as in most writers earn below the minimum wage.
Answering this question is useful because writing well requires a certain brutal honesty. It's good to begin by being honest about what you want to gain from it.