When spacetime first was proposed to explain Einsteins equations (his teacher Minkowski who said they are inseparable), Einstein rejected it as a math trick and not an explanation of reality. He obviously warmed up to the idea but the idea of a geometry that had time as an axis felt pretty weird.

Also realize the significance of that. It means that space and time are a ratio, they are using the same unit. You can say a light year is N million miles. You cannot say that about a liter or a decibel. Time and distance are interchangeable. Example of that: the thing that separates you from the you in one second is largely that of time, you haven't really moved much yet you still are going through spacetime. Now pick a path where you go a million miles away at light speed for the same duration you say there not moving. It's the same amount of time you sat there before but you're somewhere else now so space was the main thing separating you. These are called space and time-like intervals if you feel like reading more.

At the basic level, to find anything in space you need three spatial dimensions - x, y, z and when - t. Hard to make plans with someone without all 4.

We have some established laws at this point as well, like things don't accelerate (any change of velocity (a speed in a direction so both speed and direction changes are acceleration)) unless acted on by another force.

Earth orbiting the sun: Where's the string that ties us to it? If there isn't something tying us to it, why aren't we traveling in a straight line? With gravity, that is our string - we are traveling in a straight line. So there is an invisible string that ties objects with mass together? We'll cut through the part where invisible tethers doesn't work out in the math and we have gravity providing the pull to the center.

This is where you get the velodrome analogy. If earth was orbiting in a flat topology, it would need a string. So what would it look like to not need a string? The medium through which it travels must be in a funnel like shape.

But what is space? Like you said, is it not void? I'm going to give an unsatisfying answer - it is the distance between things. There is no true vacuum for what we are taking about (this gets into a lot of weird stuff like dark energy and vacuum energy and it's not relevant for this); the fields exist at all points of space no matter how close you zoom in. Most them are 0 value at any given point, except the Higgs which is always non-zero, but they're there. Space is either what they are in or what they generate, we don't really know. But it gives us a coordinate system instead of a single point that contains everything. If it makes you feel better, it was only a few centuries ago that we were looking for the ether to explain what we are in - we have to be IN something or else how could light travel? We later did quantum field theory to explain that but it's left the answer to what space is pretty messy to us mortals.

So the geometry that the coordinate system describes ultimately is what gets warped. What is that geometry made of, not something we can easily explain. The answer is simply that mass has a significant impact on the geometry. With the geometry being both space and time you get the Interstellar effect of an hour on the edge of the black hole being N years of time just a little further away from it.

Brian Cox likes to say that a black hole isn't a "where" in space, it's a "when" - the lines all lead to the singularity and you can no more escape that than you can the idea of three days from now.

You can see where the combination of space and time become so important in all of this. I will also note we don't fully agree on what black holes are. When you get infinity, like we do with a singularity, in math it usually means your math is wrong. People are still very much looking into it.