A capacitor charging through a resistor rises on a curve, not a step. The time it takes is set by the resistor and the capacitor together: one time constant, τ equals R times C, is how long it takes to reach 63% of the supply.
Raise the resistance or the capacitance and the curve stretches: the same 63% point arrives later. Lower them and it arrives sooner. The output flips on when the capacitor crosses its threshold, so R and C set the delay. This is the timing element inside a 555 timer, and it's behind many reset and debounce delays on a circuit board.