From looking at “godliness” elsewhere in scripture, and also the 1828 Websters, I think the general definition is “being like God” or usually “acting like God.” Being patient, having charity, doing good, and so forth. It is part of that familiar list: “Remember faith, virtue, knowledge, temperance, patience, brotherly kindness, godliness, charity, humility, diligence” (D&C 4:6).
So what does it mean to say that there is a power to being godly, and why does that need to be manifest? Why isn’t it more obvious? And why can it only be manifest through the ordinances and the priesthood?
Is it that the true nature of God is a mystery that the priesthood reveals, so “being like God” is something we can only understand after we know more about God?