Folding in Holdem

In hold'em, you frequently see players who call with hands they should have folded. This is particularly true when players cold-call a raise. You need a much stronger hand to call a raise than you do to raise the pot yourself. After all, calling a raise requires a hand that figures to be better than the one held by the guy doing the raising.
I've held many a hand that I was preparing to raise with, only to have an opponent snatch the rug right out from under my feet by raising before the action got around to me. Most of the time, that hand I was considering raising with is no longer even a calling hand, and winds up in the muck. When their initiative is filched from right under their noses, many players become irritated. You see it all the time, an angry slam-down of a hand like A-10 because a player raised before they could act. These players are wearing their emotions inside out. Instead of being upset, they ought to be thankful. Their opponent's raise probably saved them money, and they should be relieved, not angry. After all, money saved is just as spendable as money won, and anytime I can get a free pass out of a pot knowing my hand is probably a long shot that won't be offset by the pot odds, I'm a happy camper.
When you are faced with a raise, the hand you're holding quickly changes categories: Most likely, it becomes either a folding hand or one with which you should reraise; it's seldom a calling hand. If I'm in the cutoff seat or on the button, and someone raises in front of me, I'm going to throw away hands like A-J or A-10 - even if I would have raised with those same hands if no one had entered the pot before the action reached me. On the other hand, if I'm holding a big pair, I'm going to make it three bets, hoping to play heads up against the initial raiser. When that happens, I feel like I have a big advantage going into the flop. Not only did I get the last raise in, I'll have position on my opponent throughout the entire hand.
That doesn't mean I'm going to play that hand to the river - if, for example, I made it three bets with J-J and the flop contained an ace and a king, I'd be a fool to keep playing if there was any appreciable action. But if no overcards fall, I'm a favorite over anyone who would raise with a pair of nines through a pair of aces, as well as A-K, A-Q, A-J, and K-Q.
Later Folds
The longer you're involved in a hand, the more difficult it becomes to fold. Oftentimes, the size of the pot has grown big enough to make drawing correct, even when your chances of winning might be pretty slim. The opposite can be true, too. If you've flopped a straight draw against only one opponent in a hold'em game, chances are that you will not be getting the right odds to keep calling.
Sometimes you'll find out via the betting and raising that you are not the favorite even when you hold what ordinarily is a good hand. You might have been the aggressor before the flop with A-K, been fortunate enough to see an ace hit the board, and yet watch with shocked indignation when there's a bet, a call, and a raise before it's your turn to act. Top pair, even with top kicker, is probably not good anymore, particularly if the board contains three cards of the same suit, or an obvious straight draw. Even if there's no flush possible, one of your opponents might have made a set and is now a big favorite. You can keep calling - your opponents will love you for it if you do - or you can do the smart thing and save your money for a better proposition.
Sometimes, you'll find situations that are easy folds; other times, they are strictly judgment calls based on how well you read your opponents and your analysis of the betting and raising that's transpired before the action gets around to you. Experience helps, and so does your willingness to see things as they really are, and not play poker with a denial mindset that allows you to talk yourself into calling with top pair because some part of your brain wants to believe that your opponent really did not make a flush and your hand - top pair with top kicker - is still good despite overwhelming empirical evidence to the contrary.
What Makes Poker a Game You Can Beat?
The fact that the odds are always shifting about in poker, and that you don't have to play a hand to its conclusion just because you called a bet or two on earlier rounds, is what enables good players to win at poker. You don't have this option in table games. You make a bet and, for the most part, that bet is still working until the particular confrontation you've wagered on has ended. And even if there is a "surrender" option, guess who figures to have the better of this deal, you or the house? But in poker, you have the ability to opt in and opt out. And it's often the ability and willingness to fold your tents and steal away into the night - saved money clutched tightly in your hot little hands - that provides the resources that enable you to play another hand when you have the best of it.
I know you came to play. And getting involved in a hand and slugging it out with the guys is a lot more fun than sitting on the sidelines. But that's what you have to do most of the time to be a winning player. Watch the good players. They play far fewer hands than you do. If you don't believe me, just clock them and see for yourself. It only seems like they're always in there slugging because they play very aggressively whenever they do enter a pot, and that's what you remember. But the one play they make above all others is the simplest and most boring in poker. They fold.