Power Balance acts as a multiplier to how many resources you earn, as well as the quality of the loot earned. There are a few creatures that also check it for their own abilities (Raptor Occultist deals bonus damage equal to it, Clairavoyant Spirit grants 15% of it as a bonus to stats).
Power Balance improves by 2% for each battle won if below 200%, and 1% if above. Bottled creatures can also increase it by amounts varying from 20% to 180%, and the Pandemonium coins can either set it to your maximum or 20%.
It’s used to power teleporters and portals between realms, as well as certain overworld spells:
5% to travel to a new realm or return to one through a portal;
10% to start a new Realm dive;
15% to start at a previously accessed Realm level automatically;
and varying costs for the spells.
The short version: Power Balance is there to prevent you from teleporting down levels as fast as possible and gaining overpowered loot by avoiding monsters.