The concepts in this section aren't especially difficult since we already learned them for congruent classes of integers, however it is a lot harder to think about congruence classes of polynomials. It's especially difficult for me to see how to reduce them (which classes are equivalent) and to manipulate them in order to show this.
I think theorem 5.8 is kind of cool just because you can apply it to any field and nonconstant polynomial where you have a commutative ring with identity. I think the main reason I think that it's cool is because we already know this theorem for integers and it's convenient that it transfers over.
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