What is "the fabric" of space-time?

There was a point brought up earlier in this thread that I am still confused about. Cave diver I would appreciate any help you can give me in raping my mind around this. Mainly that as we look farther out into space we are seeing light cones from more and more distant objects. These objects all have a more distinct red shift than closer light cones. Now the explanation I have heard is that these objects, having more space in between them move farther and faster relative to us. Being that space has a repulsive force in the manner of dark energy. All this makes sense except for the part that we are seeing light cones that are from an earlier time in the age of the universe. So wouldn't we have an older universe moving faster than today? Ex: older more distant objects move very fast away, newer, closer objects moving not so fast. Is this due to the effect of space itself stretching the frequency emitted from the objects? Any help would be appreciated thanks.

Actualy I like to make up lymerics to help me remember, so raping kinda fits that and my spelling is terrible.Thank you for the explenation, that makes more sense. I tried to think of it the same way a laser gyroscope works just over much larger scales.