You can thank The Ocelot for that artwork.
I always picture the following to help me understand:
Imagine a large group of people in a room (electrons in a battery). There are two doors in the room, a wide door (labeled low resistance) and a narrow door (labeled high resistance).
A fire alarm sounds, and the people (electrons) scramble to leave the room quickly. More people can leave
through the wider door than the narrow one.
Because more electrons can freely leave the battery via the low resistance coil, it pulls more amps from the battery.
Less electrons are able to pass
through the higher resistance door (coil), therefore less amps are used.
A battery doesn't actually "work" when it gives its stored energy; it freely gives the energy to whatever source will accept it. It's when that energy is released too quickly that the electrons become over-heated and the battery gets hot...too hot...and the battery self destructs into thermal runaway.