This is a monostable multivibrator circuit, or “one shot”. The diference between a monostable and astable multivibrator is that the monostable vibrator has a default or preferred state from which it can be jostled for a only a set period of time. That time frame is determined by C1 & R2, see information about the RC time constant. In this circuit applying voltage to the trigger T will ground one of the leads of C1, causing it to behave like a short until it can charge again via R2. Q will read as voltage high during that period. It is normally off.
Again one of the sites from yesterday has a good write up:
but compare it to the circuits on these two pages:
Niether use the extra transistor, but instead apply a switch straight to the base of Q1. The capacitor on the first links page makes it nonretriggerable, I think.