This rule pertains to phosphorescence and similar phenomena.  Electrons vibrate and resonate around molecules in different modes (electronic state), usually depending on the energy of the system of electrons.  This law states that constant-energy flipping between two electronic states happens more readily when the vibrations of the electrons are preserved during the flip: any change in the spin of an electron is compensated by a change in its orbital motion (spin-orbit coupling).
Intersystem crossing (ISC) is a photophysical process involving an isoenergetic radiationless transition between two electronic states having different multiplicities. It often results in a vibrationally excited molecular entity in the lower electronic state, which then usually decays to its lowest molecular vibrational level. ISC is forbidden by rules of conservation of angular momentum. As a consequence, ISC generally occurs on very long time scales. However, the El-Sayed rule states that the rate of intersystem crossing, e.g. from the lowest singlet state to the triplet manifold, is relatively large if the radiationless transition involves a change of molecular orbital type. For example, a (π,π*) singlet could transition to a (n,π*) triplet state, but not to a (π,π*) triplet state and vice versa. Formulated by El-Sayed in the 1960s, this rule found in most photochemistry textbooks as well as the IUPAC Gold Book. The rule is useful in understanding phosphorescence, vibrational relaxation, intersystem crossing, internal conversion and lifetimes of excited states in molecules.