@kiwiheretic, good question.

I don't know how the mainstream physics answers it, but here's my personal opinion.

"Space" is only a math abstraction in order to describe the real world, as well as numbers. There are many different spaces: Euclidean space, Minkowski space, Riemann space and so on. We can apply these models to describe matter, energy and relationships between them. But no one has never observed "space", only matter and energy. When they tell "space expands" or "space curves" it's only a convenient model.