Physical meaning of curvature in relativity I understand space is not a rigid structure which actually bends (like a metal bar or rubber sheet) so "curvature" due to energy momentum pressure and stress (stress energy tensor) is??
This is were I get confused, I understand the basic functions of tensors involved (metric, ricci, reminnian, energy momentum) and that they relate the distribution of mass-energy to space time curvature, and that the basic function of the Einstein field equations is you take a quantity of energy mass IE the Sun put it into the right side of the equation turn some wheels and you get the projected geodesics of space-time in which test particles will follow?
Just can't grasp in my mind what is really happening when in reference to curvature?
Thanks to anyone who could help me along a bit :)
 A: Curvature can be interpreted in many different ways. 
For me, the most intuitive is that in a flat manifold initially parallel lines remain parallel, while in a positively curved manifold parallel lines converge. You can think of this in terms of the surface of the earth where longitude lines are parallel at the equator but intersect at the poles. This works for spatial curvature and it also works for curvature of timelike worldlines. Two objects at rest with respect to each other have parallel worldlines, and in curved spacetime they can converge without bending (accelerating). This is tidal gravity. 
Another one is in terms of angles on a triangle. In flat space the angles in a triangle sum to 180 deg, but in a positively curved manifold it is larger. For instance, if you go due north from the equator, at the North Pole turn 90 deg, go due south to the equator, turn 90 deg, then when you return to your starting point you will be 90 deg off. So that is a triangle with 270 degrees. This also works for curvature in time, but it isn’t as obvious to me. If two objects start off initially at rest then their worldlines each make a 90 deg angle with the line joining them, and when they collide their relative velocity is a spacetime angle which makes it a triangle of more than 180 deg. This is also tidal gravity. 
The last one is in terms of parallel transport in small loops. When you make a loop and you parallel transport around the loop the vector doesn’t come back to itself. I have a harder time with this one because it makes sense in space but closed loops in time don’t have a physical meaning. So I tend to think in terms of the previous two. 
