You guessed it - a power amp pedal is a floor-based unit that can emulate an amp’s power section. With one of these, you can essentially hook your entire pedalboard up to a speaker cabinet, so that you have an all-encompassing rig quite literally at your feet.
If you no longer want to lug around a heavy amp to gigs, power amp pedals eliminate their purpose and enable you to plug into a venue’s own speaker cabinet or even its front-of-house PA system for direct monitoring. The sound guy will love you for it! And like with most preamp pedals, power amp stompboxes typically feature solid-state circuitry for dependable operation.
Of course, power amp pedals gel with preamp pedals; it’s what they’re primarily designed to work with. However, it’s not like you have to use a preamp stompbox with a power amp pedal, as in fact, a lot of guitarists use overdrive and distortion pedals instead of them. This can be attributed to the blurred line between these effects, as a lot of distortion pedals can more or less do what preamps can; they boost, distort and compress your signal. You could just argue that they are sometimes marketed differently.
Some guitarists also use power amp units in conjunction with their multi-FX pedals too. Premium multi-FX and amp modelling products like the Line 6 Helix don’t necessarily need a power amp, as they can be plugged directly into compatible FRFR (full range, flat response) cabs. However, simpler multi-FX units don’t have this functionality, and therefore a power amp pedal can bridge the gap.