How to calculate the exact delay of a delayed ON/OFF imlemented by low pass filter
Your circuit is essentially a low-pass filter, filtering out the rapidly-changing high-frequency components of the step function. In the context of filters, cutoff frequency is more often used, but in the context of timing circuitry like this, it's probably better to think in terms of the time constant, $$τ=RC=\frac{1}{2πf_c}$$

The reason these are related is simple: The cutoff frequency is the frequency at which the circuit is no longer able to change rapidly enough to keep up with the changing input, and the time constant tells you how rapidly the circuit can change.