This interview question seems forward (not to mention intimidating!), but if you're asked it, you're in luck: There's no better setup for you to sell yourself and your skills to the hiring manager. Your job here is to craft an answer that covers three things: that you can not only do the work, you can deliver great results; that you'll really fit in with the team and culture; and that you'd be a better hire than any of the other candidates.
Any candidate can read and regurgitate the company’s “About” page. So, when interviewers ask this, they aren't necessarily trying to gauge whether you understand the mission—they want to know whether you care about it. Start with one line that shows you understand the company's goals, using a couple key words and phrases from the website, but then go on to make it personal. Say, “I’m personally drawn to this mission because…” or “I really believe in this approach because…” and share a personal example or two.