When you pick up a small or medium pocket pair and cold call a raise, you're almost always looking to "set-mine," which is simply the act of just trying to hit one of your two case cards on the flop and make three of a kind. If you miss, you give up and fold to any bet. No harm, no foul. You will only hit your set about one time in seven point five, so you need around eight to one in implied odds make the call.
So why do we say 15 instead of 8? Answer: the factor of fifteen is to make up for things like getting stacked by set-over-set, not getting paid off when you do hit, good opponents folding and not paying off when you hit, etc.
Another thing to note when set mining and applying 15x rule is that you’re more likely to get paid off by someone raising in EP than in LP (because they’re more likely to have a real hand). In fact, you actually want them to have a hand like AA or KK or QQ, because these are the hands that average players are more likely to get stubborn against you when you hit your set.
Also, you’re more likely to get paid off by nits that lags, bad players than good players, and so on. In other words, you can tweak the 15x rules accordingly, based on the caliber of player you’re cold-calling against and/or the range they hold. The more likely they are to pay you off (or the better their range), the closer to 8x you can go. Conversely, the less likely they are to fall into the trap of paying you and your set off, the higher the implied odds. I’ve frequently folded hands like 55 and 44 from the blinds against LP raisers that I’ve tagged as good. (But I’m also just as likely to reraise to resteal against these players, too; you should be constantly looking to maximize your EV. Sometimes, folding is the best play, while other times it’s better to fight back. Like most things in poker: it depends.)
In the next installment on this subject, I'll write a little bit about the "25" part of the rule...
All-in for now...