The reason a swimmer floats—even when relaxed and not actively swimming—is buoyancy, the upward force exerted by any fluid on an immersed object. Here's how it works:
An object submerged in fluid experiences an upward force equal to the weight of the fluid it displaces. Water weighs ~1 g/cm³ (1 kg/L). The average human body density is slightly less than water (~0.98 g/cm³) due to air in lungs, fat tissue, and bone structure. Thus, the weight of displaced water exceeds the body's weight, creating net upward force.
Fluid pressure increases with depth. The pressure on the bottom of a submerged body is greater than on the top, generating a net upward force vector. This pressure difference is buoyancy.
Buoyant force = fluid density × submerged volume × gravity. A larger volume (e.g., inhaling deeply) increases displacement and buoyancy. This is why floating is easier with full lungs.
Fish use swim bladders to adjust density; marine mammals have blubber and lung control; even ships float because their hulls displace enough water despite steel's high density.
So "uncontrolled sinking" is a misperception—unless you exhale completely and have very low body fat, your body's natural buoyancy keeps you at the surface.