"Hydrostatic" is a word that means stationary (static) water (hydro). Hydrostatic pressure is the force exerted on a surface by a stationary fluid; think of the pressure you feel on your eardrums when you swim to the bottom of a pool. Hydrostatic pressure describes pressure in all stationary fluids, not just water.
The air that surrounds us exerts a hydrostatic pressure on our bodies of about 15 pounds per square inch (air, like water, is a fluid that can exert pressure). We don't feel the hydrostatic pressure of the atmosphere because the pressure inside our bodies pushes out and balances the pressure of the air pushing in; which is to say, we are in equilibrium with the pressure of the atmosphere. When you fly in an airplane, the discomfort you feel in your ears is due to the changing hydrostatic pressure in the cabin. Chewing gum, yawning, or swallowing eases the discomfort because it opens airways in your head and lets the pressure inside your ears match the pressure outside.
In the deepest parts of the ocean, the hydrostatic pressure reaches about 16,000 pounds per square inch, or roughly 1,000 times pressure at sea level. Deep-sea creatures can withstand enormous pressures because the insides of their bodies are at equilibrium with their environments. The low pressure at the ocean's surface would be as deadly for them as a trip to the ocean bottom would be for us. Some animals, however, have adapted to enormous pressure changes. The sperm whale can dive to depths of 3,000 feet, where pressures are 100 times greater than at the surface.
One of the reasons that treating foods with high hydrostatic pressure can effectively kill certain types of microorganisms is that the treated food is brought into equilibrium with the high pressure surrounding it. That is, the pressure throughout the treated food is the same as the pressure at the surface. The pressure of the treatment for oyster bacteria is about 35,000 pounds per square inch -- double the pressure in the deepest parts of the ocean. Microorganisms sensitive to high pressure cannot hide deep inside a piece of meat, for example, because the pressure is as high there as on the outside. Other sterilizing processes, such as chemical, heat, or ultraviolet treatments, often can't penetrate deeply into bulk food.