More than likely it's "unique visitors" to the sites.
In the industry standard vernacular, "hits" refers to any http request -- if you have photos, ads, navigation buttons, includes to measure traffic, separate CSS files, java or javascript, and miscellaneous graphical doodads, you can easily reach 40 or 50 hits on one Web page. That's why almost no one uses hits as a measure of popularity.
These are terms used in measuring Web traffic. I don't expect TV reporters, or the folks who make their graphics, to know the finer points. So what they translate to "hits" I can only guess.
Page views is another metric -- one that measures only the number of main content pages users see. If you load one page with 27 8x10 color glossy pictures with circles and arrows and a paragraph on the back of each one, it counts the same as loading one page with nothing but text. My best guess is that the Nielsen numbers are page views, but without seeing the original study I can't be sure.
Then there's unique users, the number of people who visit a given site on a given day. It's a useful number, but not the end-all of measuring reach. For example, a lot of people hit NYT.com or CNN.com or Foxnews.com and never click on a link -- they skim the headlines, see that nothing important to them has blown up in the last few hours, and then go on with their day. I suspect that very few FR users load the main headlines page and then don't go deeper.
Another measure is total usage minutes -- a measure of the "stickiness" I mentioned in my last post. Web sites, like broadcasters, don't just want folks to drop by. They want them to stick around. FR is a very sticky site (and I mean that in a good way -- no need to bust out the Lysol).
It's like that in TV, too. Fox News stomps CNN in the Nielsen ratings, but by another measure -- how many people check in however briefly, what TV people call the "cumulative" or "cume" -- CNN wins. More people watch CNN for some period of time on any given day than watch Fox. But Fox viewers stay tuned longer, so there are more of them at any given moment/minute/hour.
So what's the real measure of popularity and influence? Is it better to have ten thousand viewers for ten seconds or a thousand viewers for ten minutes? It's a philosophical question. And a financial one for the advertisers who have to choose their placements.