"Mate" means the king has no means of escape.

 

"Checkmate!" is said when an opponent's king is under attack and cannot escape.

 

"Checkmate!" signals the end of the game and the player who checkmates an opponent wins the game!

 

Here the black king is checkmated by the white queen and rook.

 

Here the black king is checkmated by the white bishop. 

 

Note: the black knight is pinned.  The knight cannot take the white bishop, due to a check on the black king!