This is the best possible Hold'em hand and is known as the royal flush, which consists of the ace, king, queen, jack and ten of the same suit. It's essentially a straight flush but using the five highest cards.
This is five cards in sequential order and all of the same suit. In the event of more than one player having a straight flush, the highest rank at the top of the sequence wins. For example, 5,6,7,8,9 of clubs beats 4,5,6,7,8 of clubs.
Four of a kind, also known as quads, is a hand containing four cards of the same rank and one other card (the kicker), such as K K K K 7 ("quad Kings"). Each four of a kind is ranked first by the rank of the quads, and then by the rank of the kicker. So, quad Kings with a Queen kicker is a better hand than quad Kings with a Jack.
Three cards of the same rank, and two cards of a different, matching rank - three of a kind and a pair. In the event of a full house versus full house, the highest three matching cards wins. If these are the same for both players, then the highest pair of the players is the decider.
A flush is a poker hand containing five cards all of the same suit, but not all of sequential rank, such as Q 10 7 5 4 (a "queen-high flush").
Each flush is ranked first by the rank of its highest-ranking card, then by the rank of its second highest-ranking card, then by the rank of its third highest-ranking card, and so on. For example, K J 9 6 4 ranks higher than Q J 9 6 4. Flush hands that contain the same ranked cards but differ by suit alone (such as 10 8 7 6 5 and 10 8 7 6 5) are equal.
This hand contains five cards of sequential rank not from the same suit, such as 9 8 7 6 5 (a "nine-high straight"). In Texas Hold'em, an ace can be used as either above a king or below a two, so A K Q J 10 is an ace-high straight, and 5 4 3 2 A is a five-high straight. Straight hands are not ranked by the suits they comprise of: 9, 8, 7, 6, 5 is the same nine-high straight whatever mix of suits they come from (excepting the straight flush). As you'd imagine the stronger straights are made with the highest ranked cards, for example a King-high straight (9, 10, J, Q, K) is better than a Jack-high straight (7, 8, 9, 10, J).
Three cards of the same rank, and two unrelated side cards. The higher the card is ranked, the better the three of a kind - so three Aces is better than three Eights.
In the event of the same three of a kind, the player with the highest (or even second-highest) card wins.
If you hold a pocket pair and then hit your third matching card on the board, this is known as a set. If your three of a kind is made when you don't hold a pocket pair it's simply known as trips. They are both ranked the same, just different terms.
This is two cards of the same rank with another two cards the same as each other but of different rank, for example a pair of 8s and a pair of 9s. If players have an identical two pair hand then the kicker is the decider.
This is two cards of the same rank, and three other unrelated cards. The higher the rank of the pair, the better. In the event of players having the same pair, the player with the highest, or even second or third-highest card, wins.
This is all that's remaining from the categories above. A single card can win pots. If it comes down to single cards, the highest card wins, such as ace-high.