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.
It would be better to say that potential energy is the amount of work that a *system* can do. Say you have a system consisting of two masses - a brick and the Earth. As the brick moves down *U* decreases, the force pulling the brick and the Earth together acts downwards on the brick and it can do some positive work. On the other hand, if brick moves up, *U* increases but now the force of gravity on the brick acts in the opposite direction to its motion so it does negative work. You could imagine a stretched spring pulling the brick up. The brick would do negative work on the spring causing it to lose its *U*.