Big site - how to get more organic search traffic?

Here's a question that probably won't have a simple answer.

I'm one of the rarer cases where I get more direct visits to my site than organic search referrals. For example, today (as of the time of this post) I've received 874 direct visits and 758 organic search referrals. The ratio is usually even lower, where my direct visits are about 20% higher than the organic search referrals I get.

My site consists of user generated content, and a very large number of new, keyword-rich, pages are produced by our user base every day. In fact, we're currently at over 800,000 indexed pages.

It blows my mind that I get such a small number of organic referrals every day considering the number of indexed pages...and no single page stands out as one that drives more traffic than any other. My search traffic comes from a huge handful of random, usually long-tail search terms every day.

My links are generally optimized for SEO and I have meta tags, keywords, so I don't know what I'm missing.

What strategies could I employ to get the overall net effect of an all-around lift in my search traffic?

I speak to other sites where the ratio of site visits to search referrals is drastically different, so I'm sure there's a lot of room for improvement.

Thanks so much for any suggestions!