Auroras are natural light shows, usually seen in locations very far north or south. Although they don't have much to do with mechanical physics, they exemplify principles of magnetism, as well as the transfer of energy between different forms.
For an aurora to occur, a large amount of energy is required. This comes from solar winds, which send charged particles (mostly electrons) towards Earth. Since these particles are charged, they can't just travel in a straight line--they must follow the magnetic field of the Earth. For this reason, they usually enter near the poles. That's why auroras usually are seen near the Arctic and Antarctic Circles.
When the electrons reach the atmosphere, they collide with gaseous molecules, raising their energy. These higher-energy forms are more unstable, so the fall to the ground state is inevitable. When the energy falls, it is emitted in the form of light energy. This is the same principle that traditional neon lights utilize. The color that we see is dependent on the chemical makeup of the gas: lower altitude, molecular oxygen emits green light; high altitude, elemental oxygen emits red light; nitrogen emits blue light.
A time-lapse video of the Aurora Borealis (Northern Lights) can be seen at