We can think of a physical system as a subset of the physical universe as a whole. We define what constitutes the system based on what we are interested in analyzing. Anything outside of the system we ignore for analysis except for how it affects the system we're looking at. So for example, your body can be considered as a physical system. The solar-system can be thought of as a physical system. A lagoon can be thought of as a physical system. Even an individual atom can be thought of as a physical system. It all depends on what you want to look at.
Stability properties of a physical system refers to how the system responds to some perturbation; whether the system can recover on its own after being perturbed or whether it goes haywire. Stability analysis helps us to understand what happens when we perturb a system.