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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.
But what kind of force caused the door to open? Here is where Mechanical Energy comes in. Mechanical energy is the sum of kinetic and potential energy in an object that is used to do work. In other words, it is energy in an object due to its motion or position, or both. In the 'open door' example above, I possess potential chemical energy (energy stored in me), and by lifting my hands to push the door, my action also had kinetic energy (energy in the motion of my hands).