I'm going to assume you mean fluid (oil or liquid) powered machinery rather than fluid power generating systems such as water dams.
There are many benefits to a hydraulic system compared to other power systems.
In a pneumatic (air) powered system there are only two states, pressurized or depressurized. With hydraulics you can control the flow of the fluid and therefore control position and force quite easily.
With electrically powered system such as a motor powering a drivetrain, the motor must be at high revolutions per minute in order to provide sustainable torque. Hydraulic systems can generate high amounts of torque at low rpm. Depending on the sytem design they can also take up less space.
One hydraulic pump can also power a large variety of systems within a shop or machine via manifolds and valves. Electric systems often require one motor and gear box for every sytem. This helps to reduce cost and maintenance issues.