To defecate. Usually done in a fashion in which one must brace (his/her)self during the waves of discomfort that come over them while defecating. Other symptoms include: contortion of the face, gritting of the teeth, perspiration, quiet grunting, and/or clenching of the fists (if not grabbing on to the nearest sturdy structure).
Also: Battle the brown juggernaut, Doing battle with the brown juggernaut
Person in stall 1: "Excuse me sir/miss, you seem to be struggling extensively over there... Do you need medical attention?"
Person in stall 2: (through gritted teeth, hands pressed against stall walls) "Grr... No...I'm just battling the brown juggernaut...uggghh... I might be here for a while, check on me in 10 minutes..."