Action
The time-integral of the Lagrangian along a trajectory: S = ∫ L dt = ∫ (T − V) dt. Units of energy × time.
Definition
Action is the scalar quantity assigned to a candidate trajectory of a mechanical system. You integrate the Lagrangian L = T − V from the start event to the end event along the candidate path, and the resulting number — the action S — scores the path. The physical trajectory is the one for which S is stationary under small variations.
Action has the same units as Planck's constant ℏ; in quantum mechanics each path contributes a phase exp(iS/ℏ), and the classical path emerges as the one around which these phases stop interfering destructively. The ubiquity of action principles — from Newton's mechanics to general relativity to every quantum field theory of the Standard Model — is one of the deepest facts in physics.