In general relativity, energy bends spacetime. However, this doesn't mean that a fifth dimension for spacetime to "bend into" exists." That is, spacetime isn't embedded in a higher dimensional space, Instead, the curvature is said to be intrinsic.
But what does that mean? One could imagine the sphere on a ball as an example of extrinsic curvature it seems that intrinsic curvature isn't as straight-forward and intuitive. Is there a simple and easy way to understand the differences, and how a space can "curve" without actually be embedded in a higher dimensional space to "bend" in?