Aku = Evil
Soku = Immediate (more emphasis on "immediate" as opposed to "swiftly" or "quickly")
Zan = Slay (Depending on how you see it; literally it means "chop" but this changes slightly in context. Here it probably means "slay".
Though some may consider such a "law" an extreme measure, those who followed it did so religiously. Believing that no matter what side they fought for, that as long as they upheld Aku Soku Zan, they would accomplish their mission.