Why is a manifold called a manifold?

Question

Manifold in English means many and various. (https://www.merriam-webster.com/dictionary/manifold)

How did this come to mean a topological manifold with a differentiable structure?

Answer 1

According to Aguirre, Foster, and Merali's Questioning the Foundations of Physics, the term "manifold" comes from the German term "Mannigfaltigkeit" used by Riemann, which he used to describe the set of possible values of a variable under several constraints, because the variable can have many values. English mathematician and philosopher William Kingdon Clifford then translated this to "manifoldness."

Answer 2

Manifold is simply a fancy word for variety or plurality.

Before Riemannian (or non-Euclidean) geometry, only the flat kind of spaces was considered, aka Euclidean spaces, for each dimension. So, for instance, when a $2$-D space was concerned, it was only a flat plane and that was the only kind of space (same goes to $3$-D, etc.) Then Mathematicians (like Riemann) started to think of curved-kinds, which made an $n$-dimensional space no longer of a unique, flat kind but variety or Mannigfaltigkeit (ie, manifold in English) of dimension $n$.