while playing quake, refers to moving left or right without turning. good players assign separate left and right strafe keys while using the mouse to turn. a simple maneuver to learn is to 'circle-strafe': strafe right and turn left (or versa vice), keeping your victim in view all the time. good quake players strafe constantly and unpredictably to avoid fire.
This is the action of moving from left to right in a attempt to avoid being hit by your opponent (either real or computer controlled). Practice in this skill can be very important when playing the harder levels of difficulty. In my experience the movement is easy, what's hard is keeping the crosshair on the target whilst moving