Hello Steve,
welcome at PF. Newton introduced absolute space and ascribed to it the origin of some forces, like the centrifugal force. He also made an experiment to demonstrate that the absolute space does influence material objects: water in a jar that is at rest has a flat surface, but in rotating jar it has curved surface even when it is still with respect to the jar. I have read somewhere that he saw imperfections of absolute space, but he decided that still it is the best thing he can think of and went on with developing his mechanics.
Einstein's general theory of relativity introduced a different view on space (and melded it with time), but confirmed that it plays an important role. In this theory, the space has properties which differ in each its point (like curvature) and now even the space itself is influenced by the material objects.
These theories were very successful. However, the concept of absolute space was criticized by Mach. The basic idea of Mach is the following. He pointed out that without external objects, the water in the jar would have no way to tell that the jar is rotating. Hence it is possible that the water would be always flat. This hints that maybe they are the external objects that are responsible for the centrifugal force on the water.
Machism is a very attractive idea (it was to Einstein as well). It basically says we should not be content with the theory we have but search for better and simpler explanation. I think it would be great, if we could explain properties of absolute space - such things as centrifugal force, existence of inertial frames, or even the fact that there are three dimensions - in terms of relations between objects.
There are some attempts at building theory without the absolute space, relying only on relations between material objects. It is called relational mechanics - it is about relations between objects, in distinction to relations between objects and space, which is in general use. Unfortunately, these attempts probably were not as successful as the ordinary theory.