In addition to being a sweeeet Led Zeppelin song, buy no quarter means to show no mercy. Refuse to give an opponent the oppurtunity to quit or rest. This use of quarter is probably derived from the meaning of quarter which refers to shelter, as in head quarters. Thus, no quarter means that your opponent is offered no retreat to shelter or protection.
(Don't want to thread-jack, here, but something that may be to interest for everyone playing in this fascinating game [and why did I JUST NOW see this??]... there is a podcast called "A Way With Words" ... nerdy, but has EVERYTHING to do with this... look it up. Okay, again, sorry for threadjacking...)