Stimulated emission occurs under the specific circumstances of a population inversion, that is, when there are more electrons in a higher energy level than one below it. There will be a certain energy difference between these two energy levels.
When a photon with energy equal to the gap passes, it stimulates an electron to drop down to the lower energy level, emitting the energy it lost as a photon with the same wavelength, phase and direction (coherent with) the starting photon.
This differs from an electron spontaneously dropping down an energy level in that the photon is not emitted randomly. If this occurs many times, as in a laser, intense, coherent and monochromatic (one wavelength) is produced.