From ^{1}:

In physics, action is an attribute of the dynamics of a physical system from which the equations of motion of the system can be derived through the principle of stationary action. Action is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Generally, the action takes different values for different paths.

Mathematical formulation, via the Lagrangian:

$$S=\int dt L(q,\dot q)$$

^{1}

Wikipedia contributors. (2021, March 9). *Action (physics)*. Wikipedia. https://en.wikipedia.org/wiki/Action_(physics)