Nature is essentially "lazy." If potential energy gets converted into kinetic energy (i.e. the potential does work on the particle) then this is reflected by a change in the Lagrangian: L=T-V. Nature doesn't want to do work, so the Lagrangian should change as little as possible over the particle's trajectory. The action is the changes in the Lagrangian added up over the entire trajectory, i.e. essentially how much work was done over the particle's path. So the path that minimizes the action is the "laziest" possible path.
This argument seems to be true