When a molecule or atom in the ground state (S) absorbs light, one electron is excited to a higher orbital level. This electron maintains its spin according to the spin selection rule; other transitions would violate the law of conservation of angular momentum. The excitation to a higher singlet state can be from HOMO to LUMO or to a higher orbital, so that singlet excitation states S, S, S... at different energies are possible.
Kasha's rule stipulates that higher singlet states would quickly relax by radiationless decay or internal conversion (IC) to S. Thus, S is usually, but not always, the only relevant singlet excited state. This excited state S can further relax to S by IC, but also by an allowed radiative transition from S to S that emits a photon; this process is called fluorescence.
Alternatively, it is possible for the excited state S to undergo spin inversion and to generate a triplet excited state T having two unpaired electrons with the same spin. This violation of the spin selection rule is possible by intersystem crossing (ISC) of the vibrational and electronic levels of S and T. According to Hund's rule of maximum multiplicity, this T state would be somewhat more stable than S.
This triplet state can relax to the ground state S by radiationless IC or by a radiation pathway called phosphorescence. This process implies a change of electronic spin, which is forbidden by spin selection rules, making phosphorescence (from T to S) much slower than fluorescence (from S to S). Thus, triplet states generally have longer lifetimes than singlet states. These transitions are usually summarized in a state energy diagram or Jablonski diagram, the paradigm of molecular photochemistry.
These excited species, either S or T, have a half-empty low-energy orbital, and are consequently more oxidizing than the ground state. But at the same time, they have an electron in a high-energy orbital, and are thus more reducing. In general, excited species are prone to participate in electron transfer processes.