Absorption is a process where an atom or molecule absorbs energy to promote an electron into a higher energy level. Often, the energy is delivered by a photon. The photon must have the same energy as the difference between the energy levels in the atom or molecule.
Spontaneous emission, or just emission, is the reverse process. An electron drops to a lower energy level and loses energy, which is emitted as a photon. As the name implies, this process happens spontaneously, so the photon is emitted with a random phase and direction. In stimulated emission, an incoming photon stimulates an electron to drop to a lower energy level. This creates a second photon that has the same phase and direction as the first photon.