I know the operation of the diode but I still can't understand how it works
What I understand about potential difference
  
  The basic electronic says a source voltage is the result of a
  potential difference between its poles.  


It is more practical to consider a voltage source as an element having electric potential energy, which is manifested through a potential difference between its terminals, and has the ability to move electric charge.


  With that I understand that a battery of 1.5V has a positive terminal
  with 1.5 volt charge and a negative terminal to 0 volts of charge.


The Volt is the unit used to measure electric potential or potential difference. To measure amount of electric charge, the Coulomb is used.
The fact that a battery is 1.5 volts, means that the potential difference across its terminals is 1.5 volts, and is a measure of the battery capacity to do the work of moving electric charge, or that is, generate an electric current.


  What I understand about diode
  
  A diode is a semiconductor electronic component divided into two
  poles, one negative and one positive so with a potential difference
  between them; It is separated by a resistive layer between the poles.


The diode is not divided into two poles, but it consists of semiconductor material N type and P type These materials are obtained from pure silicon, by adding impurities (doping), which provide electrons (N type) or generate holes (P type).
This device doesn't presents a potential difference between its terminals, ie, if we connect a voltmeter to the terminals, there will not measure voltage. The associated quantum effect is the Potential Barrier. Basically this is a distribution of the electric potential energy in the crystal lattice formed by silicon, which acts as a barrier that prevents the passage of electrical charges, whether these holes or electrons.


  When a diode is connected to battery directly (negative diode with
  negative source) etc, free electrons on the negative side of the
  battery repel the electrons free from the negative side of the diode
  to destroy the resistive layer and the current flow through the
  circuit.


The connection that you describe, is called forward bias diode. Nothing in the internal diode is "destroyed". What happens is that the potential energy of the battery is greater than the energy implicit in the potential barrier, which, it is reduced, allowing the passage of electrical charges.


  What I can not understand
  
  Let's say I have a source with 0 volts in its negative pole and a
  diode with -7 volts in its negative pole. Logically, the electrons on
  the negative side of the diode should go to the negative side of the
  source and thereby increase the depletion layer in the diode even when
  polarized directly to the source.


I guess you're talking about a 0 volt battery with the positive terminal and -7 volts on the negative terminal. In this case the only thing that interests us is that the difference in potential corresponding to this battery is 7 volts. Then in the application with the diode, the only thing we care about is whether it is forward bias or reverse bias.
Charges of equal polarity repel, so free in the N type materials electrons are repelled when connected to the lower potential pole. In this case, it is forward biased.
Different polarity charges attract, so that the free electrons in the N-type material are attracted when connected to the pole of higher potential battery. In this case it is reverse biased.