There is a detailed discussion of what you need to know about Hubbard model here
Note that this is entirely my guess of how examiners interpret the syllabus.
Domains, you will recall (see chapter 21 of book), are large regions of a magnetic material where all the magnetic moments are aligned. In a macroscopic sample there will be several domains with moments potentially misaligned with each other. The interface between domains is the domain wall.
If you apply an external magnetic field some of the microscopic moments flip over -- the way this happens is by some domains growing and others shrinking -- or in another language, the domain walls move around (this is domain motion).
What is crucial is that unless there is some sort of disorder in a macroscopic system, if you remove the external magnetic field the domains move right back to their original configuration and you have no net magnetization. The only way to get the domain walls to hold their position is to have disorder that "pins" the motion of the domain wall. This can freeze in magentization and give you M not zero even in B=0.
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