the principle of least action

Of all the conceivable paths a system might take between a fixed starting and ending configuration, nature selects exactly one. The principle of least action says the chosen path is the one for which a certain quantity, the action, is stationary, usually a minimum. It is as if the system surveys every possible path and picks out the extremal one.

Precisely: hold the endpoints q(t1) and q(t2) fixed, and among all paths joining them the physical path makes the action S = integral of L dt stationary, meaning delta S = 0 to first order in small variations. This single variational condition is exactly equivalent to the Euler-Lagrange equations, which for a mechanical system reproduce Newton's second law.

Honestly, 'least' is a slight misnomer. The action is stationary, not always a minimum; over long times it can be a saddle point (past a conjugate or focal point), which is why 'principle of stationary action' is the more careful name. Deeper still, it is the classical shadow of quantum mechanics: Feynman's path integral sums e^(i S / hbar) over all paths, and the classical trajectory is precisely where the phase S is stationary so that nearby paths interfere constructively.