A metastable state of excitation (i.e., a metastable energy level of an orbiting electron) is one that lasts longer than typical, e.g., lasts seconds, minutes, or hours rather than a tiny fraction of a second. Examples:
Metastable states are often a part of forbidden lines: they are often so delicate that any disturbance will cause them to relax, and are unlikely to live out their undisturbed life unless unlikely to come near to another molecule, e.g., in a near vacuum.
Metastability is actually a more general concept, i.e., that small disturbances result in negative feedback, but some possible disturbances on a larger scale would receive positive feedback, i.e., lead to instability. In quantum mechanics, the potential "disturbance" can be a quantum-mechanical probability of a change, and metastability results in much longer half lives (which is a way of expressing what happens to electrons in metastable orbits). The structure of an atomic nucleus (nuclear isomer) can be in a metastable state: an arrangement of the nucleons which is not at the minimal energy level, resulting in radioactivity with a long half life (but in the case of nuclei, the "long half life" may well be a tiny fraction of a second).