The physical interpretation is simply that one is adding a controller that, combined with the dynamics of the plant, causes the overall system to be stable. What this means in real systems is changing the eigenvalues in the software controller, as most controllers are in software-based contexts.
As far as changing eigenvalues physically, unless you change the dynamics of the plant system itself (i.e. change or move parts, add actuators, etc.), the eigenvalues of the plant remain the same. It's the closed-loop eigenvalues that you're changing around.