Why is light emitted when electrons move from the excited state to the ground state?

The most common way for electrons to move to an excited state is by absorption of electromagnetic radiation. When an electron absorbs this radiation, it takes in the energy that the wave contains and this causes it to move to a higher energy state. They come back to ground state at the first possible opportunity because in the excited state they have lots of potential energy. Electrons can make different jumps in energy levels when it loses this potential energy (ie. it can go directly to the ground state, or it can go to lower energy levels and then the ground state). When they move to lower energy levels, the electrons emit the electromagnetic radiation that was absorbed - the frequency of the waves emitted depends on the electron's jumps between energy levels as it returns to ground state.