The duration of the pulse is called the time period (T) and this is determined by resistor R1 and capacitor C1
A monostable circuit produces a single output pulse when triggered. It is called a monostable because it is stable in just one state that is output low state. The output high state is temporary. 

The duration of the pulse is called the time period (T) and this is determined by resistor R1 and capacitor C1
 

1 The output (pin 3) goes high (near Vcc) when the 555 receives a trigger input

In the monostable this occurs when the switch is thrown, in the astable when the power is turned on and the capacitor is initially discharged

2 It stays there until a threshold reaches 2/3 rd of supply

This is determined by the capacitor and the resistor(s) in both the astable  and monostable shown above 
Note the threshold is always connected to the capacitor for both circuits
 

The time this takes to occur in the monostable  is determined by R1 and C1
In the astable, capacitor C1 charges, resulting in a voltage drop across R1 and R2.
When the voltage at the threshold reaches 2/3 of the supply(Vcc) a transistor inside the 555 turns on and discharges the capacitor.
The capacitor discharges to 1/3 rd the Vcc which in turn then triggers the input

Not that it is required at this level - but if you at the lest interested it what is happening inside the 555 then click here

else not then continue

3 at this time the input goes low (near ground)