The buoyancy force acts upward through the center of gravity of the displaced volume, primarily due to pressure differences in the fluid. When an object is submerged, the pressure increases with depth, creating a net upward force on the object. This upward force is effectively a "hole" in the water or a negative weight, stabilizing the system by positioning denser objects at the bottom and less dense ones at the top. The discussion also emphasizes that buoyancy is not significantly affected by depth in incompressible fluids like water. Understanding these principles is crucial for grasping the mechanics of buoyancy.