The composition and density of the atmosphere and the altitude of the aurora determine the possible light emissions. When an excited atom or molecule returns to the ground state, it sends out a photon with a specific energy. This energy depends on the type of atom and on the level of excitement, and we perceive the energy of a photon as colour. The upper atmosphere consists of air just like the air we breathe.
At very high altitudes there is atomic oxygen in addition to normal air, which is made up of molecular nitrogen and molecular oxygen. The energetic electrons in aurora are strong enough to occasionally split the molecules of the air into nitrogen and oxygen atoms. The photons that come out of aurora have therefore the signature colours of nitrogen and oxygen molecules and atoms. Oxygen atoms, for example, strongly emit photons in two typical colours: green and red. The red is a brownish red that is at the limit of what the human eye can see, and although the red auroral emission is often very bright, we can barely see it.
Since there is more atomic oxygen at high altitudes, the red aurora tends to be on top of the regular green aurora. The colours that we see are a mixture of all the auroral emissions. Just like the white sunlight is a mixture of the colours of the rainbow, the aurora is a mixture of colours. The overall impression is a greenish-whitish glow. Very intense aurora gets a purple edge at the bottom. The purple is a mixture of blue and red emissions from nitrogen molecules.
The green emission from oxygen atoms has a peculiar thing about it: usually an excited atom or molecule returns to the ground state right away, and the emission of a photon is a matter of microseconds or less. The oxygen atom, however, takes its time. Only after about a 3/4 second does the excited atom returns to the ground state to emit the green photon. For the red photon it takes almost 2 minutes.