There is a legend how king Stjepan Držislav won his freedom back by defeating Venezian ruler Pietro II Orseolo. in 3 games of chess after his capture, so he took "chessboard" as a coat of arms for himself and Croatians.
The White stripe has a shield of 2 rifles to represent protection if there's war, the olive branches represent peace, and the quetzal bird represents independence when the other countries separate...