Simple terms to help one understand Texas Hold'em:
Hole Cards - the cards in your hand. Only you see them and only you play them
Community Cards or "The Table" - the five cards useable by all players to make their best hand
Flop - the first three cards on the table
Turn or Fourth Street - the fourth card
River or Fifth Street - the fifth and final card
Betting happens at 4 times during a hand.
Pre-Flop - after Hole Cards are dealt but before the Flop
After the Flop
After the Turn
After the River
Common betting terms:
Bet - duh
Raise - duh
Fold - duh
Call - match the last bet or raise
Check - Can be done when the player isn't required to call anything either because they already have enough money in, or no one has bet anything so they are willing to let it go aroudn without increasing the amount of money in the center (the Pot).
All-In - putting everything one has into a bet (or a call if the current bet or raise is more than the person has).
Common Starting Hands (Hole Cards)
Pockets - a pair in your hole cards
Bullets or Pocket Rockets - Aces
Cowboys - Kings
Ladies - Queens
Big Slick - Ace King any suit
Suited - same suit (i.e. Big Slick suited is AK of the same suit)
There are other hand combos and names for them like Dolly Parton (9 5 - i.e. 9 to 5) and Doyle Brunson (10 2 - the hand he won a World Series of Poker with).
A couple other terms:
Ante - an amount all players must put in the pot if they want to play the hand. Normally only used in tournaments during the latter part. Early tuournament, cash games, and sit-n-gos rarely have an ante.
Small and Big Blinds - The basic stakes of the hand. The first player to get cards (in front of the dealer button) has to put in the small blinc ("post the small blind") and the one to his left has to post the big blind. Anyone who wants to play the hand when they see their cards must at least put in the amoutn of the big blind, and the minimum raise before the flop is the size of the big blind. So if the big blind is $5, then the minimum someone could raise to would be $10. If the betting makes it all the way aroudn to the big blind and no one raised it, the player has the option to check (see above). If it makes it to the small blind and no one has "come in" (put in the amount of the big blind to stay in the hand) the small and big blind have the option to "chop it" and take back their bets and the hand isn't played.
Play progresses clockwise around the table and the dealer button moves, along with the blinds, one seat clockwise each hand.
Final group of terms:
Showdown - that is where all the betting is done and if two or more people are still in it, the winner has to show his cards to collect the pot
Chopped Pot - When two or more hands are of equal strength, the pot is divided evenly. This can happen when the best hand is on the board or when a straight or full house "draw" (3 or 4 of the cards needed to make the hand) is on the board and two or more players "make the draw" (have the cards needed to make up the hand).
Busted draw - needing one more card to make a hand and not getting it. Often heard with straight or flush (see below).
Nuts - The best hand possible based on what is on the board
Bad BEat - When a really tough to make hand is beat by an even tougher to make hand. For instance, a full house is beat by four of a kind or the ultimate, four of a kind is beat by a straight or royal flush (see order of hands below).
Finally, the order of hands from highest to lowest:
Royal Flush - 10 J Q K A all in the same suit
Straight flush - 5 numerically consecutive cards all in the same suit (i.e. 7 8 9 10 J all hearts)
Four of a kind or "quads" - all four of a given card (i.e. all the Aces or all the Kings)
Full house - 3 of one card and 2 of another (i.e. 3 Kings and 2 Fours) - this is normally read as the three oif a kind full of the two of the kind. In our examples Kings full of Fours.
Flush - any five cards of the same suit, highest card wins
Straight - 5 numerically consecutive cards of any suit
Three of a kind, a set or trips - Three cards of the same face value. Set is sometimes used to refer to two of the cards being the players hole cards or that is also called a "hidden set" in some circles.
Two pair - Literally two cards of one face value and two of another. - A Very dangerous hand if more cards are yet to be dealt as it can turn into a full house with as high as a 17% probability if two cards are still to be dealt, but can also be easily beaten if one of the pair is on the board as someone could have the set.
One pair - just two cards with the same face value
High Card - obvious
That's a primer of terms. I won't get into the detailed game play asyou can look that up online and it gets rather lengthy.