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The Chess Pieces:

King: It's all about him! The object of the game is to force your opponent's king into a spot where he cannot escape capture, a.k.a. "checkmate" him, or else force him into a position where he cannot move without putting himself into check. 

The most valuable piece on the board (lose him and you lose the game), the king is also the most limited in his moves. He can travel only one square at a time in any direction, diagonally or horizontally/vertically along the board.  (The only exception to that rule is a cool little move called "castling" which may take place once a game). 

Queen: once one of the weakest pieces (read Birth of the Chess Queen for more info), the modern queen is a powerhouse.  She can move in any direction, diagonally or horizontally/vertically along the board, and as many spaces as she wishes so long as one of her own men is not blocking the way.  Let your queen be captured, and you're minus the strongest and most versatile member of your army.

Bishop: the sly bishops (you get two of them) zip along the diagonals either backward or forward.  Each is confined to the color on which he begins the game (one black and one white).  They are excellent team players and often move in for the capture when your opponent is distracted by one of the more flashy pieces on the board. 

Note that the bishop piece did not always represent a man of the cloth.  As Leonardo pointed out to Dino during the live chess match in THE QUEEN'S GAMBIT, in 15th century Italy the bishop was usually known as the standard bearer, and the metamorphosis into a clerical symbol was an English invention.

Knight: usually represented as a horse's head, the knights ride in pairs, too.  Like a mounted soldier, they move a bit more differently than those pieces traveling on foot.  Their movement is an L shape...two squares in one direction, and then a single square either to the right or the left of their original path.  And, like men on horseback, they can jump over other pieces as they move (the only chessman to do so).

Rook:  often (albeit incorrectly) known as the castle because of its turret-like shape, the sturdy rook is a powerful piece.  It moves horizontally or vertically as far as it wishes to go, so long as one of its fellow pieces is not blocking its way. 

Unlike the bishops, the rooks (you get two of them, as well) are not confined to a color but can move all over.  They also are the other half of the clever play known as castling, where a king and castle can swap places so long as no pieces stand between them, and neither has yet moved during the game.

Pawn: there's a reason that people in a helpless situation and/or being unwillingly (or not) manipulated by others are known as pawns.  Each side's eight pawns are the weakest of the pieces and are usually the first victims of the game, often deliberately sacrified to gain a tactic advantage (see the description of the queen's gambit). 

They're able only to move forward and but one space at a time...most of the time!  On their opening move, pawns can move two spaces instead of one.  And, when they capture another piece (how satisfying for a lowly pawn to capture a queen!), they do so on the diagonal.  But pawns are like superheroes in disguise.  Should they survive the trek to the opponent's back row, they become another piece...which one is up to the player, but the choice usually is another queen!