Welcome to the pressure section!
Pressure is Force per unit area OR: P=F/A
This can be pounds per square inch, or Newtons per square meter, etc. Under the water, two different sources exert pressure on a diver: the weight of the atmosphere on the water and the weight of the water column itself.
In a classic experiment, an Italian guy named Torricelli demonstrated that the pressure of the atmosphere at sea level could hold up 760mm / 30in of mercury in a vacume tube. Check out the picture to the left.
So the pressure at sea level is called 1 atmosphere (ata) of pressure, and it is equal to 760mmHg / 30inHg / 14.7psi or 1 bar. This device is called a barometer, and is used by meteorologists.
When a diver is at a depth of 10 meters the total, or absolute, pressure on the diver is 2 ata. Most instruments are set to read zero out of the water, so the gage pressure the diver would read on the instrument at 10m would be 1ata.
The picture at the top of the page shows, "keeping the temperature constant, the volume of a gas varies inversely with the absolute pressure (PHYSICS Algebra/Trig, Third Edition, page 435)." This is Boyle's Law, and can be shown mathematically: P1V1=P2V2
Where P = pressure, V = volume, and the subscript 1 and 2 mean initial and final respectively. So the initial pressure times the initial volume, equal the final pressure times the final volume.
Gases, such as air, can be compressed into a smaller volume, according to the Boyle's Law. This is what happens when your SCUBA tank gets filled. The air molecules are squeezed closer together so that they take up less space. This increases the pressure inside the tank.
This is important for a diver to know because, if they take a full breath of compressed air at 10 meters, they will breathe in the same amount of air molecules as two full breaths at the surface due to the increased pressure. If you try and hold your breath and come up to the surface, you are likely to pop as the gas expands with the decreasing pressure. So you should obey the golden rule of diving: Always breathe.
Liquids, like water, can be considered uncompressible for the purposes of recreational diving.