An explosively pumped flux compression generator is a fancy name for something that makes really big electric currents using explosions.
Think of it like blowing up a balloon. When you blow up a balloon and then let it go, it flies around the room because there is lots of energy stored inside. The explosively pumped flux compression generator works kind of the same way, but instead of air, it uses explosives to create a big burst of energy which gets turned into electricity.
This machine uses an explosive to compress a metal coil as tight as possible. When the metal coil is compressed, the magnetic fields inside of it get really, really strong, and this creates a massive electric current. That current can be used to power all sorts of things like lights, computers, and even cars.
It's kinda like the superhero Iron Man. Iron Man has a suit that he wears which gives him superpowers, just like the explosively pumped flux compression generator gives us really powerful electricity.