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.
The decrease or increase in potential energy is converted as mechanical work either to increase or decrease it's kinetic energy (we are considering here conservative systems). Suppose you have a system at rest at some height above the ground level, say, a ball placed on the top of a mountain. The work done in order to bring the ball of mass m to a height h on the top of the mountain is given by mgh which is stored as the potential energy of the earth-ball system. However, the displacement of earth towards the ball (by Newton's third law) is so small that you can't possibly imagine. It will be less than the size of a proton!!!. Can you imagine that? Some huge body of radius 6000 km displacing about a distance comparable to the size of a proton. So we say that the work is entirely stored in the ball's potential energy.  

Such a body is said to be in unstable equilibrium. The potential energy is maximum which indicate a less stable state as the potential energy is something that refers to a strain. Any disturbance will hence drive off the body to a state of lesser potential energy, thereby attaining stability. But the ball cannot destroy the excess energy. All it can do is to convert it's potential energy to kinetic energy, which makes the body move. Hence the potential energy decreases and the kinetic energy of the ball increases. An increase in kinetic energy means that a positive work is done on the ball by the force of gravity since both shares a common direction (or 0≤θ≤90). You can measure the kinetic energy of the ball by measuring the the work done on the ball (which is the work-energy theorem). So here we have a decrease in potential energy which corresponds to a positive work. This is very well valid with the equation.  

Now we consider the second case. A ball is now raised to a height of h meters. Initially, the body was in stable equilibrium with a minimum of potential energy. Now we have increased it's potential energy. For that, we have to do work against the force of gravity. The force of gravity is acting vertically downwards while the displacement is vertically upwards(or 90≤θ≤180). So here the work done by the gravitational force on the ball is negative. But here we have increased the ball's potential energy, which is again valid as compared to the equation.  

So an increase in potential energy corresponds to a negative work on the body while a decrease in potential energy corresponds to a positive work on the body. You should note that the sign convention is all based on the direction of displacement when compared to the force of gravity acting on it.