Depending on where you live, the mains power is 100 - 240V AC, which won't work for effect pedals. Most guitar pedals take 9V DC power, and that's the stuff that needs to be supplied for the pedal to work, and that's what you need a power supply for. Some small pedals can also be powered by an internal 9V battery, but not all. The Big Sky does not have an internal battery, it needs a power supply.
A power supply can either provide 9V DC power for a single device, like this one:
But if you have more than one effect pedal, and especially if they're in a so-called pedal board, you won't want to have a dozen separate wall warts, so you might want to use a power supply with multiple 9V outlets:
Nowadays there are rechargeable battery packs that work as power supplies for guitar pedals, a lot like commonly used cellphone and USB battery packs. Some of such battery packs can sometimes provide 9V DC power for multiple effect pedals for several hours.
Things like this
Combined with a battery-powered guitar amp, you have a truly mobile live setup! For example Roland AC-33 or Boss Katana Mini. Or many of them for a really wide stereo sound. These things actually sound incredible.
(Lucky you with a Big Sky! I settled for Boss RV-6, which is a lot cheaper and smaller and sounds fantastic.)