The prime objective for each player (whether playing as White or as Black) is to reach checkmate. Checkmate is reached by putting the opposing player’s King under an immediate direct attack by one or more of the player’s Queen, Bishops, Knights, Rooks, and/or pawns. Often checkmate is simply referred to mate

An immediate direct attack on an opposing King from a single piece or pawn is called check. An immediate direct attack on an opposing King from a single piece or pawn is called check. Such an attack also may occur simultaneously by two pieces, or a piece and a pawn, which is called – double check

When a King is in check (whether single or double), the player may not make a move or advance a pawn that does not get his or her King out of check

Checkmate occurs when a King is in check and:

• Cannot safely move to another square (i.e., without getting into further check on the other square or is blocked from moving to that square because the player’s other King is sitting on a square adjacent to that square), and
• The attacking piece or pawn cannot be captured, and
• Cannot block check: the player with the King under check by an opposing piece has no other piece that may be moved or a pawn that may be advanced to be interposed on a square to block the direct line of the attack between an attacking piece and the King.

When checkmate occurs, the player who checkmated the opposing player’s King wins the game.

While it is customary for a player to declare check, this is not obligatory under FIDE’s Official Rules of Chess.

There are certain types of checks and checkmates given special labels: fork check, double check, combined fork check & double check, discovered check, & discovered checkmate

Briefly (these concepts will be expanded upon in later tutorials), a fork check is when an opposing King and an opposing piece or opposing pawn are both simultaneously under attack by a player’s piece or pawn (the King of course being in check). A double check is when the opposing King is in check by two pieces or a piece and a pawn. A combined fork check & double check is where the King is attacked by two pieces, one of which is also attacking another opposing piece or opposing pawn (fork). A discovered check is when a player moves a piece or pawn, and another of the player’s pieces puts the opposing King into check. A discovered checkmate is when a player moves a piece or pawn, another of the player’s pieces puts the opposing King into check, and the opposing King cannot escape the check and hence is checkmated.