The secret to understanding the demographics is this: for any given category, a site's demographics score is the ratio of that category's representation in the site's audience, to that category's representation in the total population of folks who use the internet.
That's a mouthful, and I learn best from simple examples, so let's explore the meaning of that statement with a goofy scenario. Let's pretend that the internet is used by just two types of people: the Greens and the Reds. And let's say that the entire population of people who use the internet consists of just six Greens and eight Reds, like in the picture at left.Now let's imagine a hypothetical site on our tiny internet: ilovegreen.com, and let's suppose that the audience for this site consists of the three Greens and two Reds shown in the picture at right.
What would Alexa say about the popularity of ilovegreen.com among the demographic of Green users? Well Greens visit the site at a rate of 3-to-2, while they are represented on the web in general at a rate of just 6-to-8. If you like math, you can divide these rates to see that Greens visit ilovegreen.com at a proportionally higher rate than they surf the web in general; in this simple example, Greens are over-represented in ilovegreen.com's audience by exactly a factor of two. In other words, ilovegreen.com is popular among Greens. (Don't worry: if you don't like math, you'll see below that we publish our demographics data as a handy graphic which captures all the raw numbers in an intuitive way.)Remember, the fact that this hypothetical site scores high with Greens doesn't tell you about the absolute number of Greens who visit the site. What it does tell you is that Greens are represented in the site's audience to a much greater extent than they are represented out there on the web in general. In that sense, this site is preferred by Greens.
Now that we've gotten the hard part out of the way, let's have some fun. First, let's check out some sites for which we might already have pretty good guesses as to their demographics. In the charts below, a red bar pointing to the left means a category is proportionally under-represented in a site's audience; a green bar pointing to the right means a category is over-represented. So how about ufc.com, the homepage of the Ultimate Fighting Championship?

No surprises here: ufc.com is overwhelmingly preferred by young men. That is to say, men between the ages of 25 to 34 are strongly over-represented in the audience of ufc.com, compared to how they are represented on the internet at large. For the most part, these young men have college educations (or at least they're working on it), they tend not to have kids, and when they're surfing the web for news about, say, Yoshihiro Akiyama (one of the biggest mixed martial arts stars in Asia) they're doing it from home.
Now how about a site on the opposite end of the spectrum? Here are the demographics for nordstrom.com:

I know my sister spends a lot of time there, and apparently she's not alone. The audience for nordstrom.com contains college-educated, 25 to 34 year old women to a much greater extent than does the general internet population. And they tend to do their shopping from work! I'm sure it's on their lunch breaks...
A couple of more no-brainers, while we're at it. What do you suppose is the age distribution for folks who frequent the official website the U.S. Social Security Administration?

You guessed it: the users of ssa.gov skew toward web-surfers in their golden years. And what about folks at the other end of life's journey? Well, you might guess that their parents do some browsing over at landofnod.com, a retail site specializing in kids' furniture. So what do our data have to say about landofnod.com's audience?

Sure enough, they've got kids.
But enough confirming what we might already have guessed. Alexa's all about web discovery, right? Let's do some discovering. One thing folks certainly use the internet for is to find... each other. Three of the big players in the internet dating game are match.com (Alexa rank 359), chemistry.com (Alexa rank 6,517), and plentyoffish.com (Alexa rank 410).
Now imagine you're searching for that special someone, and you want to stand out among all the riff-raff. Check out the gender distribution of match.com:

Men and women are represented at match.com in almost equal proportion to their representation on the internet at large. For a high traffic site, that means there are plenty of men and plenty of women -- so if you're a man trying to stand out among men, or a women trying to stand out among women, you're out of luck. But never fear! Alexa's here to help you, ahem, improve the odds.
Compare the gender distribution of chemistry.com:

to that of plentyoffish.com:

Compared to the general internet population, women are over-represented at chemistry.com, while men are over-represented at plentyoffish.com. So if you're looking for boys, go where the boys are. And if you're looking for girls, go where the girls are!
Perhaps this wasn't what you had in mind when we said that Alexa's data gives you a competitive edge, but then again, who's complaining?