When water (Hydro) falls down through the turbine blades of an electricity generator, the blades are made to spin. The blades are connected to a shaft, which is connected at the upper end to the armature of a large generator, which produces electricity.
Most, if not all, hydroelectricity is produced in tall dams on rivers. Examples include Hoover Dam in Nevada, and Grand Coulee Dam in Washington.
The electricity produced in dams is no different from electricity produced in other ways.