It's a Lagrangian, so this is the function nature tries to minimize. In common everyday systems, the Lagrangian is kinetic energy minus potential energy.
And with the more important nitpick that this Lagrangian is a quantum operator rather than a number. In some sense nature does try to minimise it even so, but I never got an intuitive grasp on what that sense is.
I don't think that's true when dealing with the formulation in terms of path integrals as we do here...
The fields, the Langragian, and the scattering matrix are all operators; but of course their matrix elements are numbers. The path-integral formulation is a good -- and I think physically well motivated -- trick for calculating those matrix elements in terms of merely fields and their associated Largrangians.