it can be, I think of a manifold (probably naively) as the mathematical abstraction that you end up with if you start from Euclidean space and fiddle with different features - e.g. if you're in a Euclidean space how do you get from one point to another - what are the minimum requirements? What if we want calculus to work what are the minimum requirements? If we're on a surface and we walk around is there any way to tell what shape that surface is?
A generalized surface in arbitrary dimensions. A common English "surface" maps naturally to a 2D manifold embedded in 3D space.
Ok, so a manifold is simply a hypersurface. At least I‘m pretty sure in machine learning it means exactly that.
A hypersurface is usually a codimension one object, while a manifold can have bigger codimension or even not be embedded in an higher dimensional space at all
Ok, a line in 3D space can also be called a manifold? Maybe a better question is then to ask, what is not a manifold?