Hi Kelsey,
This is a good question! The most simple answer is that different atoms in Earth's atmosphere will glow in different colored lights. The aurora is made when particles from space hit Earth's atmosphere (60 miles above Earth's surface) and cause it to glow. When different types of gas are hit with the particles, they glow in different colors: red, green, blue, yellow... etc.
The tricky thing is that gases can glow in different colors and what colors they give off when they glow depends on the energy of the particle that hits them as well as how they release that energy. For example, oxygen gas with just one oxygen atom, will glow in both red and green and these are the colors most often seen in the aurora. This is how we know there is oxygen gas 60 miles above Earth's surface. Nitrogen gas with two nitrogen atoms will glow in many colors, such as red and blue.
Laura