A system very similar to pneumatic systems. Instead of using compressed air, it uses a liquid - often an oil. This is clearly in the use of the prefix hydro (meaning water) in the name.
Hydraulic systems offer greater strength and stability than pneumatic systems, although their construction can be more difficult. Where you can just release the pressure on air, and let it vent, you wouldn’t want a robot spurting vents of oil after every motion. You see, a liquid cannot be compressed to the extents a gas can, and forms a much less compliant system.
Most JCBs and other roadworks vehicles use hydraulic systems to operate. You can often here the pump going into overdrive as they move. Some heavy vehicles even use hydraulic systems for steering. Most car brakes are also based upon a braking system, hence why it is so disastrous to have a brake fluid cable cut.
With hydraulic systems, you cannot use the same valves, cylinders and fittings as a pneumatic system. They often require higher operating parameters, and stronger fittings to deal with the greater pressure and the viscosity a liquid may have that an air system would not. They occasionally need to be bled in case of pockets of air, or water condensation get in and other impurities which could cause the system to fail at best, or become quite damaged at worst.
It is unlikely that hydraulic systems would be used in a robot that is smaller than a car. At the small scale, a pneumatic system would be a great deal more appropriate, unless it is looking to lift very heavy loads like fork-lift or an exoskeleton.
Common Hydraulic System Components