In Fowler's own words, mind style must be a consistent and contextual demonstration of the views of the world by a character. It must do so in a way that shows
“cumulatively, consistent structural options, agreeing in cutting the presented world to one pattern or another, to give rise to an impression of a world-view”.
Mind Style is not an easy concept to understand so let's not confuse it with focalization or point of view. They are related to it, but not the same.
Whenever a writer wants to focalize on one character, thus showing the reader how this character understands the world around it, he or she (the author) often gives the character a unique way to express itself, so that the reader can discern several things about the character that go indirectly characterized.
A good example would be George and Lennie in Of Mice and Men. Notice how each character is linguistically represented based on each of their life experiences, cognitive levels, exposure to the world and to malice. Without explaining too much, the narrator does not need to tell us that Lennie is mentally challenged, nor that George is a tad more life-savvy. All comes together when we witness their speech, how they use it, and how they apply it.
At a metalinguistic level, the mind style also reveals a lot about the author and his or her own views of life, temperament, and their capacity for rage, or even mercy.
Notice that, in the same example Of Mice and Men, Steinbeck is forgiving toward Lennie in the way that he narrates the accidental killing of Curly's wife.
Lennie's other hand closed over her mouth and nose.
Steinbeck hints at us to understand that, as he owns the power of omniscience as an author and as a third person narrator, he could very well decide whether there is malice and intention behind Lennie's actions. As such, he has chosen to take the agency of the action away from Lennie, and he instead placed it in his hands; the hands of a man who is mentally challenged, brusque in both action and thought, and clueless about his own strength.
Does Steinbeck tell us any of these? He does not have to. He shows clearly what the mind style of each character is, particularly Lennie's. It is now the turn for us, as readers, to commiserate with Lennie and George because we, too, understand the mind style of these two sad men. We understand that Lennie will suffer the consequences of having accidentally killed a woman who was nothing but trouble in the first place.
We are able to sense the inevitability of his fate because we also understand that George and Lennie lived off a dream that would never come true. All of these emotions are not conveyed by descriptions alone. They are powerfully submitted through the linguistic structures that makes each character unique. Surely not every writer can do this effectively, which is the reason why some works of literature are superior to others.