There are vendors who specialize in characterizing your Site's traffic. Very roughly they work by finding the closest match to your Site from among a large population of Sites in which they do in fact have detailed demographic data. To improve the matching, some of them give you a javascript snippet to insert into your Site's pages to collect user data and send it to their servers (more or less like web analytics code).
Quantcast is such vendor. The link i included will take you to their page that displays sample audience demographic reports.
Crowd Science is another.
Neither of these are free (though they might have a freemium service, i don't know.
Alexa, on the other hand, is free and offers similar data; just enter your Site's url in their textbox, then when you get the results page, select the Audience tab.