1) In scientific terms, it is cause by ions within the atmosphere getting excited from the energy released by the sun. During the state of excitement, the ions release those energy in order to stabilize themselves. Those energy bear different colors, which depends on the composition of the ions. (i.e. oxygen, nitrogen, carbon, etc.)
2) In common terms, pretty lights in the sky that can only be seen at the northern regions of the globe.
Person A: Hey! Did you see the Aurora Borealis in the sky last night?
Person B: The wuh?
Person A: Northern lights...
Person B: Oh! You mean that was northern lights? I thought I was high.