An important property of fluids is pressure. Suppose we imagine surrounding a given volume of fluid (liquid or gas) by a container. The atoms and molecules of the fluid will bounce off the walls of the container, thereby changing their velocity. This change of velocity, by Newton's 2nd law, comes from a force, which is the action of the wall on the molecule. By Newton's 3rd law the molecule exerts an equal and opposite force on the wall. The pressure of the fluid is defined as the average force of the molecules on the wall per unit area:
Given a large volume of fluid, you can image putting a wall anywhere within the fluid, so that pressure is not something that is just defined at the boundaries (i.e. by the container), but is in fact defined, and can be felt or measured throughout the fluid. This is why the pressure increases as one goes down in the ocean - as one descends, there is more and more fluid above, which exerts a larger and larger force on a given area. Similarly, the pressure in the atmosphere, is quite literally due to the weight of the air over our heads pressing down on us. As one goes up in altitude, there is less air above and the air pressure decreases. The forces due to air pressure are very large near sea level: 100,000 Newtons per square meter of force pressing against us. The reason we don't implode is that the pressure of fluids inside our body (blood in veins, air in lungs etc) is equal to the pressure from the atmosphere outside, and there is no net force inward. However, slight pressure changes can have devastating effects. This is why diving too deep underwater can be dangerous. The extra pressure due to the weight of the water over your head causes huge forces which can literally crush you. This also explains why deep sea divers must have air under high pressure in their tanks. This way the air that they take into their lungs is approximately at the same pressure as the water pushing inward on their lungs, which would otherwise collapse.