This article is pretty good. A short summary is that electricity is like a sound wave propagating thru a sea of electrons or protons or something charged.

This is however the tip of the iceberg. The real mystery is how those electrons and protons feel each other. They don't bump into each other like atoms in the air, they interact via magnetic field - a mysterious medium that magically appears around charged particles and alters their trajectories. It's the same magnetic field that surrounds bar magnets. Rumors are magnetic field is made of photons, but nobody has been able to see or catch those photons, so they have been renamed into virtual photons. Those special photons don't really exist, but still interact with charges.