It's a complex subject and that article is about a fairly advanced characteristic of regulators and supplies, but if I understand your question, you are just asking what a discussion of frequency response is doing relative to DC power supplies, right?
So, the short quick answer is that it is a way of describing the ability of the regulator or supply to react to changes in either the input voltage or the load. A regulator should filter out any variation in the supply voltage (ripple) and also keep the voltage constant even as the load current varies. A standard regulator, like an LM7805, is good at suppressing 50/60Hz ripple, but if you feed it with a supply with high frequency ripple, say 1 MHz, it doesn't react quickly enough to filter that out. Likewise, if you have a load that goes on or off too quickly, it won't react fast enough to prevent a dip or surge in the voltage. Another way of looking at is to compare the regulator to an amplifier and say that it has a 'frequency response' curve. A regulator with an extended frequency response will react more quickly to supply or load variations and then can filter out noise and ripple that occurs at higher frequencies. Does that help?