How Chess pieces move and a few descriptions of commonly used terms.
Chess Pieces: King, Queen, Bishop
Chess Pieces: Knight, Rook, Pawn
Castle -- For an unmoved King to move two squares towards an unmoved Rook, and the Rook to move to the King's other side. The King may not be moved in, though, or out of check. No other pieces may be between the King and the Rook.
Check -- The player's King is in danger of being captured
Checkmate -- The player's King is unable to get out of danger. Game ends in a loss.
En Passant (In Passing) -- Pawn moving two squares may be captured by adjacent Pawns as though it only moved only one square, but only on the immediately following turn.
Files -- Columns on a board, denoted by letters a to h, from White's left to right
Promotion -- A Pawn advancing to their farthest rank is replaced by the owning player's choice of Bishop, Knight, Rook, or Queen.
Ranks -- Rows on a board denoted by numbers from 1 to 8, from White's side row to Black's side row
Stalemate -- Occurs when the active player has no legal moves, but isn't in check. Game ends in a draw.
Wikipedia played a large roll in the gathering of this information.