An electron shell is a spherical region around the nucleus of an atom where electrons can orbit. Due to the quantum nature of angular momentum (angular momentum can only take certain values which come into play at small distances and masses), electrons cannot orbit just anywhere around a nucleus and the possible radii are termed shells. Around a nucleus is a smallest shell, then a surrounding larger shell, and another, and so on, and each such shell has a maximum number of electrons that can occupy it. Associated with each shell is an electron quantum number termed the principle quantum number (or radial quantum number), often listed as n, which can be thought of as numbering the shells outward:
|shell name||shell's n||limit on electrons in the shell||if all filled|
For other reasons, no shell is actually populated with more than 32 electrons.
Electrons can occupy a higher shell than they need to, in which case the atom has a higher-than-minimal energy (atomic excitation), and an electron may spontaneously shift to the lower shell, the lost energy going into an emitted photon, and conversely, an incoming photon can lift an electron from its shell to a "higher" one. Between any two shells is a specific energy-difference, and the tendency of certain frequency photons to be emitted or absorbed by an atom is due to these energy differences.
Molecules have more complexity in electron orbits.
The electron shell concept is used in quantum mechanics, as an explanation of an atom's inner workings, in chemistry, to explain certain elements' tendency to interact, and in spectroscopy, to explain and interpret spectral lines.