Mostowski’s Collapse Theorem (lemma) states that any well-founded and extensional relation $E$ on partially ordered class $P$ is isomorphic to a transitive class and $\in$.
My question is that why it is called collapse theorem because the content seems have nothing to do with collapse.
It is instructive to think about the collapse of a set of ordinals.
Suppose that $A$ is some set of ordinals, its collapse is its order type. Why? We map the least element of $A$ to $0$, and then the next one to $1$, and so on.
In the general case, this might be a bit harder to visualize, but we sort of collapse the ranks of the members of the class to their "correct value".