Ive heard someone say powermetal gets its name from the fact that the music is very anthemic and majestic that it "empowers" the listener. It is also very powerful sounding music in its own right. Theres a lot of energy, speed, and bombasticness (is that even a word? lol) in it.
I wouldnt consider Maiden powermetal, but they were definately one of the forefathers of it. Id say the big influences you hear in power metal are Maiden, Priest, old Scorpions (Uli Roth era), Manowar, Rainbow, Deep Purple, Dio, Black Sabbath, Ozzy...that kinda stuff. Then bands like Helloween, Running Wild, and Rage came along and they really started the whole sound that we think of when we hear the name powermetal. They dont all sound the same either, you can have more straighfoward barebones ones like Hammerfall, more commercial ones like Stratovarius, more neoclassically influenced ones like Angra, or bands that are sort of a mix between power and prog like Symphony X.