The product of RC(=220n*220K=48.4ms) introduces a time constat, by which "leftsideofswitch" approaches toward node3.
It means that "leftsideofswitch" would not reach node3 immediately.
I think that this RC path acts as a debouncer. You can search for the concept of "contact bounce".
So, when the switch is pushed, it takes 48.4ms for "leftsideofswitch" to reach 0v or 6v. Consequently, it takes a ratio of 48.4ms to reach 2v and 4v which are critical voltages for 555 to change its state. Using this, one could be sure that the output would not fluctuate during the "short moment" when the operator holds the pushbutton.
If RC is too much, then it will not let you to toggle one state after the other after a short period. If RC is too small, then the task of debouncing will not be accomplished.
So you can use other values near these R and C, however, appropriate values are determined depending on type of pushbutton and frequency of switching.