Take a system, any system. The system could be a particle (a point with a precise location but no inner structure), a rigid body, a field, or what have you. Now imagine all of the possible histories the system could undergo. (The histories don't have to span all of space and time; you could choose two temporal endpoints for the history, or, if it's a field, some spacetime region in which the history happens.) That gives you a space of histories; call it W.

The action is a map S from histories in W to real numbers: it assigns each history a number. The details about how it does that depends on the dynamics -- or perhaps better: how it does that constitutes the dynamics.

As you wander around history space W, you'll find that there are certain histories at which S is stationary: i.e. S doesn't change much at all as you mildly perturb -- locally explore around -- the history you're at. Those histories are special according to S; call them stationary histories.

The action principle says: the stationary histories are all and only those histories that are possible for the system to undergo. All of the other histories are impossible.

We need the action principle only insofar as all classical systems appear to obey it -- for some choice of S. It might not seem very remarkable that you can find some S to do that, but what's remarkable is that S always tends to take a pretty simple form. In particular, it tends to privilege histories which can be determined, at any time, by the system's configuration and how fast that configuration is changing at that time.