Question: Potential energy can be thought as the amount of work that the force can potentially do on the point because of its position. $$W=-\Delta U=U\_{initial}-U\_{final}$$

A positive work done by a force translates into a negative variation of potential energy. That sounds ok, given the interpretation of $U$ stated above. If a force does some work, then the "potentiality" of doing more must decrease.

But the equation says also that any time the force does a negative work, the potential energy increases. Why does this happen, in the light of such interpretation of $U$?

Answer: 
If a force does **negative work**, it is in fact trying to work against another force, doing **positive work**.

When you lift up a book from the floor, gravity does *negative work* on the book, while you do *positive work*. And the books rises higher up, so $U$ increases.

* Negative work just means "**receiving**" instead of "**giving**" away energy. Which basicly is the same as saying that *something **else** is doing work on it*.

There is not more to it than that.
Work done is $\vec F \cdot \Delta \vec x$.  

If $\vec F$ and $\Delta \vec x$ are in the same direction then the work done is positive.  

If $\vec F$ and $\Delta \vec x$ are in opposite directions then the work done is negative. 

Consider a spring fixed at one end as a system and an external force $\vec F$ stretching the spring. 

If the external force $\vec F$ stretches the spring a little more then the work done by the external force is positive and the elastic potential energy in the spring has increased.

On the other hand with that external force $\vec F$ acting on the spring if the spring length is reduced then the external force has done negative work and the elastic potential energy of the spring has decreased. 

Suppose that the external force was produced the gravitational attraction of a mass at the end of the spring.  

Now assume that the mass and the Earth are the system.  

The spring is producing an external upward force on the mass and Earth system.

If the spring contacts the spring has done positive work and the gravitational potential energy of the mass and Earth system has increased.

If the spring stretches the spring has done negative work and the gravitational potential energy of the mass and Earth system has decreased.