The brakes on your car, the lift in the mechanics shop and standard construction machinery such as front end loaders, back hoes, and bull dozers all require hydraulics instrumentation to perform their function. In addition to this, all sorts of industrial cutters, presses, folders and a substantial amount of manufacturing machinery depend on hydraulics. Hydraulic technology is pretty important to our standard of living seeing as how we depend on it in so many ways to perform many tasks for which we either directly or indirectly rely upon.
Hydraulic technology largely is dependent on the fairly good approximation that liquids are incompressible. This means that if you put a liquid under a great deal of pressure, it will not shrink but will take up the same amount of volume it had prior to being placed under pressure. Hydraulic fluids also have to be used inside of moving parts and not leak through high pressure gaskets without breaking down itself or anything else through chemical processes and so commercial hydraulic fluids are designed to maximize these desirable qualities in the fluid.
The process used in hydraulic technology starts with recognizing that when put under pressure, hydraulic fluid has an extremely small shrinkage which takes place. This means that if a volume is completely filled with hydraulic fluid, if one spot touching that liquid is caused to pressurize the liquid, that pressure is felt throughout the entire liquid.
Consider a sealed U tube filled with fluid, if one end of that tube was a piston, you could push on the piston to apply pressure to the entire liquid. So even if the piston had only a surface area of a square inch and the entire tube had an area of 100 square inches, that entire larger area of 100 square inches will feel the same pressure that was applied from the 1 square inch piston.
If the second side of the U tube also had a piston attached, that piston would feel any pressure applied by the first piston. If the first piston still had only a 1 square inch surface area touching the liquid, if the second piston had a 100 square inch area, then putting a pound of pressure on the first piston of 1 square inch area will cause a full pound of pressure per inch on the larger 100 square inch piston. This device is now a fully functional hydraulic lift, the 1 pound of pressure on the small piston applied a full pound of pressure on every inch of the large 100 square inch piston meaning that the larger piston could now move 100 pounds instead of the 1 pound input pressure applied.
The difference is compensated by the amount of distance each piston moves. If the small piston moves one inch in to apply the pressure, the larger piston will only move a hundredth of an inch to lift a full one hundred pounds. So the trade off is in that a small pressure over a long distance can result in large pressure over a very small distance (such as from your brake pedal to the brakes on your car).
In this way, a hydraulic system can convert a small force (over a long distance) into a very large force (over a very small distance).