Deeper means higher pressure
Dive to the bottom of a swimming pool and your ears begin to ache within a couple of metres. Nothing has grabbed you; the water is simply pressing harder. The reason is beautifully simple: every layer of fluid must hold up the weight of all the fluid stacked above it. Go deeper and there is more weight overhead, so the pressure climbs. This depth-dependent squeeze is hydrostatic pressure.
Let us turn the picture into an equation. Imagine a column of fluid of cross-sectional area A reaching down to depth h. The fluid in that column has volume V = A h, so its mass is m = \rho A h and its weight is \rho A h g. That weight presses down on the area A at the bottom, adding a pressure of \text{weight}/A = \rho g h on top of whatever pressure P_0 was pushing on the surface above.
The hydrostatic equation: the pressure at depth h equals the surface pressure P₀ plus ρgh. Here P₀ is usually the atmosphere pressing on the top of the fluid.
Only depth matters — not the shape
Notice what the equation does not contain: the area A cancelled out, and so did the shape of the container. Pressure in a fluid depends only on the vertical depth below the surface. A narrow straw and a vast lake, filled to the same depth, have exactly the same pressure at the bottom. This is the famous hydrostatic paradox, and it is why any two connected points at the same level sit at the same pressure — which is precisely why water finds its own level and why a spirit level works.
Gauge versus absolute pressure
There are two ways to quote a pressure. Absolute pressure counts from a perfect vacuum; the diver above was at $1.3 atm absolute. **[[gauge-pressure|Gauge pressure]]** counts from the local atmosphere — it is the *extra* pressure above the surrounding air, and it is what a tyre gauge or blood-pressure cuff reports. The two are related simply: absolute = gauge + atmospheric. A tyre inflated to “200\text{ kPa}$” is really at about 300\text{ kPa} absolute.
The hydrostatic equation is also how we measure pressure. A barometer balances the atmosphere against a column of liquid: P = \rho g h lets a height stand in for a pressure. Mercury, at 13{,}600\text{ kg/m}^3, needs a column only 760\text{ mm} tall to balance one atmosphere — which is why 760\text{ mmHg} became a pressure unit. Try the same with water and the column would have to be over 10\text{ m} tall, which is exactly why a suction pump cannot lift water higher than about ten metres.
Pascal's principle and hydraulics
Now squeeze a fluid that is sealed and (like most liquids) essentially incompressible. Because the fluid cannot shrink and cannot resist a shear, any increase in pressure you apply at one place appears undiminished at every other place in the fluid. That is Pascal's principle, and it is the working heart of every hydraulic machine.
Picture a hydraulic press: two pistons of different area connected by oil. Push gently on the small piston (area A_1) and you raise the pressure everywhere by \Delta P = F_1/A_1. That same pressure pushes up on the large piston (area A_2) with a force F_2 = \Delta P \, A_2. Equating the shared pressure gives the hydraulic law.
Pascal's principle applied to a hydraulic press: the output force is the input force multiplied by the ratio of piston areas.