The deeper the object is placed in the fluid, the more pressure it experiences. This is because is the weight of the fluid above it.
Add to this - the weight of the fluid, INCLUDING THE AIR above it.
Air compresses, so we have the phenomenon of thinner air at higher altitudes. You do NOT get thicker water with depth, the water is not compressing. The water is the same volume, but because it is being pushed down by all the stuff above it, the water is under pressure. Put something down there with anything compressible in it and the water will try to force that same thing to compress until it's at the same pressure as the water.
25 years ago I was on a submarine in the Navy and dealt with this all the time. One neat trick was to take a soft 8 oz styrofoam cup and trap it in a free flood area outside the hull. While we were underwater and deep, the air was squeezed out of the cup. After surfacing, the 8 oz cup would come back as a little 1 oz shot glass and no longer soft. All the air had been compressed out of it by the surrounding water.
Some easy numbers. These are not exact, but are good estimates. Pressure at sea level is approximately 15psi (Pounds per Square Inch). When go under water, that pressure goes up by 15 psi every 33 feet that you go down OR 45 psi for every 100 feet. If you scuba dive to 100', you are breathing air that is at 60 psi because that is the weight of the water and air above you. If you held your breath and swam for the surface, the pressure on the air in your lungs would go down, the air would expand and your lungs would burst because you have about 4 times as much air as you can hold at the surface.
You can see the same thing with a beach ball - take the ball and swim down 20' into a deep pool. The ball will become flat because the weight of the water is pushing in on the ball, compressing the air until the volume decreases to the point that the air pressure equals the weight of all the water and air above it. At 20', roughly 20 psi.
Air compresses. Water does not.