Why does potassium give off a purple flame in flame test?

Potassium gives off a lilac purple color due to the energy level configuration of the potassium atom. When heated the electrons become excited to higher levels of energy. When they "move" to a lower energy state, they give off energy in the form of light (photons). The color seen by your eye is a combination of certain specific colors (frequencies) of photons. It is the same as when you hear a musical chord. It is actually a combination of several different musical notes (frequencies).