Concrete example for the definition of parallel inheritance

While reading Dive Into Design Patterns by Alexander Shvets, I stumbled across the following statement in the section "Favor Composition Over Inheritance":

Trying to reuse code through inheritance can lead to creating parallel inheritance hierarchies

According to this site the definition of parallel inheritance is the situation in which subclassing a class requires creating yet another subclass elsewhere. I'm interested in knowing what would be this kind of scenario, where we'd have to subclass all over the place, and further more the why of it: why would we have to create the subclass elsewhere? Does the need arise from the context and the problem we are trying to solve, or is it induced by the structure of the (at least) two class hierarchies and composition between them? While here is an attempt to give a mathematical definition for the parallel inheritance, the need for the implication is not clear to me.