Double check
Two pieces attack the king at the same time.
Check and an opened line
One way to give double check is to move a piece off the line of your rook, bishop, or queen. If the moving piece also attacks the king, both pieces give check at once.
What to check in reply
Only a king move can answer double check. The king may capture one of the checking pieces if the capture square is safe. If there is no safe king move, it is mate.