Value of Hands

The basic values of 5-card poker hands are, in order from best to worst :

Straight flush, five cards of the same suit in sequence, such as 76543 of hearts. Ranked by the top card, so that AKQJT is the best straight flush, also called a royal flush. The ace can play low to make 5432A, the lowest straight flush.
Four of a kind, (aka quads) four cards of the same rank accompanied by a "kicker", like 44442. Ranked by the quads, so that 44442 beats 3333K, and then ranked by the side card, so that 4444A beats 4444K(*).
Full house, three cards of one rank accompanied by two of another, such as 777JJ. Ranked by the trips, so that 44422 beats 333AA, and then ranked by the pair, so that 444AA beats 444KK(*).
Flush, five cards of the same suit, such as AJ942 of hearts. Ranked by the top card, and then by the next card, so that AJ942 beats AJ876. Suits are not used to break ties.
Straight, five cards in sequence, such as 76543. The ace plays either high or low, making AKQJT and 5432A. "Around the corner" straights like 32AKQ are usually not allowed.
Three of a kind, (aka trips or a set) three cards of the same rank and two kickers of different ranks, such as KKK84. Ranked by the trips, so that KKK84 beats QQQAK, and then ranked by the two kickers, so that QQQAK beats QQQA7(*).
Two pair, two cards of one rank, two cards of another rank and a kicker of a third rank, such as KK449. Ranked by the top pair, then the bottom pair and finally the kicker, so that KK449 beats any of QQJJA, KK22Q, and KK445.
One pair, two cards of one rank accompanied by three kickers of different ranks, such as AAK53. Ranked by the pair, followed by each kicker in turn, so that AAK53 beats AAK52.
High card, any hand that does not qualify as one of the better hands above, such as KJ542 of mixed suits. Ranked by the top card, then the second card and so on, as for flushes. Suits are not used to break ties.

(taken from the rec.gambling.poker FAQ).

When you're judging how good your hand is, it's important to realize what's "out there" and how your hole cards are playing. In general, you want to be using both your hole cards to make your hand. If you're just "playing the board" (using all 5 cards on the board), then your opponents have *at least* as good a hand as you, so you're playing to tie at best. Similarly, some hands (like a pair of aces) can either be very good or not so good depending on the board.

On the pre-flop round, you only have your 2 hole cards, so you don't yet have a poker hand at all. The best hole cards you can have are AA (pocket aces). The next best is KK (pocket kings). In general, any "pocket pair" is pretty good, but low pocket pairs are not very good on their own. Any two high cards is pretty good, like KQ or AJ, but the concept of "domination" is important (more on all this later). At this phase your hole cards are all about their potential to make a hand.

On the flop, there are now 5 cards out, so you can make a poker hand. You'll always at least have a "high card" hand. There are also 2 more cards to come, so your hand has the potential to improve. For example, you might have a 4-card flush, which is worth nothing on its own but has good potential to become a 5-card flush, which is very good. On the turn, you have 6 cards, so there are several ways to make a hand, and some potential to improve. On the river, you have your final hand.

Hands that use your hole cards well are better than those that don't, because it makes it less likely that you can be beat. For example, having two-pair using both your hole cards is stronger than if there's a pair on the board. That is, consider these two cases :

1) You hold a 9 and a 7. The board shows 9,7,Q ; your hand is 9977Q - two pair 9's and 7's with a Queen.
2) You hold a 7 and a Q. The board show 9,9,7 ; your hand is 9977Q - the same hand!

You have the same hand in both cases, but in case 1 you like your hand better. The reason is that in case 1 there are fewer hands that beat you! The only hands that can beat you are a better two-pair (such as a 9Q hole) or three of a kind (a set), such as QQ in the hole. In case 2, any pocket pair above 7's beats you, such as 88 in the hole. Also, any higher 7 beats you, like 7K and 7A, and any 9 beats you - 9X.

Eventually you will be thinking along the lines of "Bayesian Poker" which we will discuss in the future.  

Consider this simple example :

You have 33 in the hole.
That's a decent hole, heads up, you are probably currently in the lead.
The flop comes 67Q with two spades.
Now your current hand is 3367Q , so you have just a pair of 3's, not a very good hand, but perhaps still winning heads up.
The turn comes a 3 of spades.
Now your current hand is 3337Q , you have a set of 3's, that's a very good, it's almost surely winning.
The river comes the T of spades, so the board is now 67Q3T with four spades.
Your hand is now 333TQ, a set of threes.
Your hand is now not very good, because there are four spades on the board and you don't have a flush.

This shows how your hand can change value dramatically as the board changes.  Do not get attached to your cards or get a fixed idea of how valuable they are.

At any point, the best possible hand is "the nuts".  What the nuts are depends on what's on the board.  If a straight flush is possible, it will be the nuts, but often the necessary cards aren't on the board.  If there's a pair on the board, the nuts are four of a kind.  The "2nd nuts" is the next best hand, etc.  The best possible hand of a certain type is "the nut" of that hand, for example the best flush is the "nut flush".  Generally the nut flush is the ace-high flush, but with an Ace on the board, it's the person with the King in their hand, etc.