Royal Flush
The five highest ranking cards of a suit. A Royal Flush is essentially an Ace high Straight Flush.
Straight Flush
Any five cards of the same suit in consecutive order. The example is a five high Straight Flush. (Only the Ace can be high or low for Straights).
Four of a Kind
Four cards of the same rank (for example, 4 Kings), with one dissimilar card.
Full House
A triple of one rank plus a pair of another. The example is Queens over Twos, which beats Jacks over Aces because the triple is taken first.
Flush
Any five non-consecutive cards of the same suit. (If they are consecutive, you have a Straight Flush).
Straight
Any five consecutive cards of mixed suits. Ace can be high (next to a King) or low (next to a 2) but not both at the same time.
Three of a Kind
Three cards of the same rank (a triple), with two dissimilar cards. (If the other two made a pair, you would have a Full House).
Two Pair
Any pair of one rank, plus any pair of another rank. If two hands have the same high pair, the second pair decides the winner. If both pairs tie, the remaining high cards decide.
Pair
Any two cards of the same rank. When two hands have the same pair, the remaining high cards decide.
High Card
If no other hand rank is achieved, the highest card held wins. If two hands hold the same high card, then remaining high cards decide.