"Most people", sure, but most people *here*...?
I mean, by pure calendar years, our oldest and feeblest members are probably Ash, the Gryge, perhaps Hugh and Rand and... Idunno, something like that order(*). I hope you're not saying *those* guys wouldn't understand a concise explanation like my attempt below? Except I suspect most of them know this already:
Web site owners often want or need to keep track of who has visited their site and some details of the visit (when, which pages, how many pages this month, etc). One way to do that is with "cookies", little snippets of data that the site's Web server sends to the user's browser to keep. Since each browser keeps its cookies stored in its own way, a user who has several browsers on the same machine also has several different sets of cookies on that machine. For places like the NYT, who want to keep count of how many pages you've visited for free, this means that the user can browse his allotted number of pages *in each of his browsers*, so for example having three different browsers installed means you can read thirty NYT pages each month in stead of ten.
Except of course, as has been pointed out above, opening a link to such places in an "incognito", "private" or "anonymous" -- or what have you -- tab or window is even better, since that means any cookies get discarded after you close that session. (Thus you can in effect circumvent that policy totally, subject only to the limitations set by your own conscience.) In both FireFox and Chrome the menu you get when you right-click a link has an "open in private window" choice; the one in Internet Explorer (version 9 here) does not.
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(*): Sorry to any greybeards who feel left out; 'tis naturally only because I've been misled by your youthful on-line demeanour. Or youngsters I promoted in age; that again is of course due solely to your impressive aura of intellectual maturity.