A euphemism for a girls period. "Angry pants time" is the time when a girl is usually more irritable than others and has a tendency to be "angry" often.
#1: Man, Carly's being a real bitch lately.
#2: Yeah, she has, must be angry pants time.
A pair of pants that are horribly uncomfortable to the point where anyone wearing them is grumpy for the rest of the day. Angry pants can only affect certain people.