What is Lagrangian and action?

The Lagrangian of a mechanical system whose forces derive from a potential energy $E_p$ is the function of the coordinates, the velocities, and possibly the time

kinetic minus potential energy, both expressed in the generalized coordinates. The action of a conceivable motion $q(t)$ between fixed endpoints $q(t_1)$ and $q(t_2)$ is the number

$S$ is a functional: it eats a whole path and returns one number, in joule-seconds — the units of Planck’s constant.