The monostable, aka one-shot, configuration generates a single pulse of a predetermined length in response to a trigger.
At rest, the trigger input will be high (in this case that means > 1/3 Vcc) and the output will be low. This means that the Q-bar output from the flipflop will be high, which turns on the discharge transistor keeping C1 empty and the threshold voltage at 0v.
When the trigger input goes low briefly (i.e. falls below 1/3 Vcc) the trigger comparitor sets the flipflop, making its Q-bar output low. This turns off the discharge transistor allowing C1 to charge through R1. It also causes the output to go high.
C1 charges through R1 until the threshold voltage reaches 2/3 Vcc. Recall that this will take RC seconds. When it gets to that point, the threshold comparitor resets the flipflop, making Q-bar high. This makes the output low, and turns on the discharge transistor which grounds the discharge pin. Since this is connected directly to the point between the capacitor and resistor, the capacitor discharges essentially instantaneously. This also causes the threshold voltage to go to zero, and the flipflop's reset input to go low. Now both the set and reset inputs to the flipflop are low and the circuit is again in a stable state with the output low.
In summary, taking the trigger low briefly causes the output to go high for the length of time defined by RC. Below is a diagram showing the temporal relationship between these various signals.