A capacitor is an easy and inexpensive way to create a delay in analog circuits.
Along with a resistor you have an adjustable R x C time constant.
You can get different kinds of delays, depending on how you arrange the RC, and which component you take a volt (or current) reading from.
It takes a lot of words to describe a delay fully and unambiguously. I can suspect what is meant by 'power on delay'. I'll have a better idea if you say 'power is delivered to IC 5 seconds after power is applied to timing circuit'.