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If a potential energy can be associated with a force, we call the force conservative. Examples of conservative forces are the spring force and the gravitational force. If a potential energy can not be associated with a force, we call that force non-conservative. An example is the friction force.
When we put work into the mass m, that energy is converted to a capability to do future work. In a sense, the work we put into the mass when lifting it against gravity's force can be put to use later; so it is stored as potential energy. So, using the conservation of energy law WE = Wh = mgh = PE.