A quantum mechanical system or particle that is confined spatially can only take on certain discrete values of energy, called energy levels.
This contrasts with classical particles, which can have any amount of energy.
The term is commonly used for the energy levels of electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules.
The energy spectrum of a system with such discrete energy levels is said to be quantized.