Why can a capacitor connected to ground in a 555 astable circuit change pin 2s output?
I recommend you to watch the video again and again.
Basically, changing the C value in question delays the time taken to set or reset the output. It is basically a RC circuit. Resistor and capacitor in series. The voltage across the capacitor rises and the time taken to rise is defined by the equation \$RC\$ 

 

The capacitor takes more time to reach 1/3 rd of VCC as the capacitor value increases. This produces the delay in the output.