The sun gives off not only light and heat, but also a stream of charged particles. These particles are called the "solar wind". Earth has a magnetic field that has a clear sense of directionality, which is why a compass works. Charged particles can act like magnets and get pulled along the lines of Earth's magnetic field and build momentum. When they bump into some of the atoms in the air (usually oxygen or nitrogen), some of their momentum can turn into energy; this energy can be given to the atom that they bump into. The atom doesn't like having extra energy, so it finds a way to give off the energy, usually as a packet of light.

Auroras are formed high-energy particles (mostly from the sun) getting deflected by the Earth's magnetic field and channeled into the upper atmosphere near the poles. The impact of these particles with the ionosphere excites the air, and creates the colors and patterns visible from the ground (or from space). I don't know a whole lot more about them, but given that this is plasma physics, it's likely that not much more *is* known.