n00b: "Oh $hit!"
"None given or asked." Replied his opponent.
The cannons on these fighting ships were usually placed along the sides, the stern section housing officer quarters. So, to say you will give or show no quarter, is to basically say you will not allow the ass end of your vessel to line up with the guns of your foe. Such condition would leave your vessel most vulnerable.
It is interesting how I used the word quarters to describe the officer berths above. This made me think, as I'm sure the meaning of this term also implies "take no prisoners". This same meaning could easily have come from the days of sail as well.