Atomic excitation (or electron excitation) is the state of an atom whose electrons are at a higher energy level than their ground state, i.e., a state of excitation. It is also the attainment of such a higher state.
The atom's possible electron orbits are determined by quantum physics, and are quantized, or only allowed at certain energetic states. With sufficient energy, e.g., from a incoming photon, an electron can be moved to a higher state (a higher electron shell than they need to be in), i.e., an excited state. Such an excited atom will eventually emit a photon and move toward its lowest state, i.e., its ground state, such a change being called electron relaxation.
Radiated excitation is the energization of the electrons of an atom by a photon, i.e., bound-bound absorption. Gas excitation is the energization of atoms in a gas.
The absorption of photons to excite atoms results in absorption lines and the subsequent return of atoms to less energetic states results in emission lines, e.g., hydrogen's Lyman series.
The term population inversion refers to a group of atoms where the majority are in an excited state.