How is bound charge and free charge possible?

Imagine a blob of liquid water. Each molecule is polar because the electrons are closer to the oxygen than the hydrogens. Without a large external electric field, the water is moving around bumping this way and that way with basically random orientations.

Now while in orbit make a very large parallel plate capacitor,charge it up and put your blob of water in between the plates. They still move around and bump into each other, but now if the hydrogen side is pointing in the direction of the electric field, it becomes harder (energy wise) to change that orientation. Over time the water can start to develop a preferred net polarization. How strong can depend on the temperature as well as the strength of the field. This is your polarization. Im your mind imagine looking at a line through the water and if the field was much stronger than the temperature induced vibrations you might see the individual charged parts of each water molecule line up like

• +- +- +- +- +- +-

where each +- is the two charged sides of a water molecule, so they are always always next to each other. And to someone that only cared about net charge they might look and see that it looks like

• +.....................-

So it might look like there is only some surface charge. But that plus on the one end is bound to the negative part right by it and that negative one (on the other side of the surface) is bound to the positive part right next to it.

Now no water is pure, so you can imagine putting salt in the water and some of the NaCl crystals really do break up into Na and Cl ions (even the water itself has ions, some of the H20 molecules break up into H and OH ions) and those ions really have a net charge each and they can move around. Those are the free charges, in an external field they can move around (as charge carrier for a current, or going to the surface) and these positive and negative charges really can be far away from each other.

The bound charges aren't just affected by the parallel plate capacitor, they are affected by each other and by the free charge, but if you didn't care about the bound charges because you only care about the ions and electrons that can be added or removed from the water, then you can work with the displacement field $\vec{D}$ that ignores the bound charge. Then you get something that tracks what you care about.

An example is a high-dielectric capacitor. If all you care about is how it works as a capacitor, and you don't care about where each polarized molecule is located, then you can compute the $\vec{D}$ field inside just like for a normal capacitor.

A dielectric is not a conductor, thus there are no electrons that are able to flow through it. However atoms or molecules within may be able to be polarised making an electric dipole, which can align to enhance or anti-align to reduce the applied field. This is bound charge.

In a metal or in free space the electrons flow and are, in a sense, free. They are able to move around independent of any fixed atom.

I suppose there will also be (but not in any course I ever did) materials in which there exist charges that are able to move (free) and those that are stuck together as atoms to be polarised (bound). Your book may include into the free definition anything that is not a neutral atom being polarised.

Editing in response to an update of the question look at the Wikipedia page for curl: http://en.wikipedia.org/wiki/Curl_%28mathematics%29. If in any of the pictures you imagine that at each point where there is an arrow, there is an atom with electric dipole moment in the magnitude and direction of the arrow. From this you can see how there may be a curl in the polarisation.