R only affects the charging/discharging time of C and therefore the output frequency. It does not affect the threshold.
R1 and R2 function as a potential divider, so that when the output of the amplifier swings from V+ to V-, the voltage on V2 swings by a smaller amount.
When the voltage on the capacitor (V1) reaches the threshold (voltage on V2) the output switches.
Note that the amplifier output will not usually reach V+ or V-. There will be a small voltage drop. See the amplifier data.