Its easy to find out what the structure of the Earth is, grade school stuff:
https://en.wikipedia.org/wiki/Structure_of_the_Earth
I apologize if this sounds condescending, but I will attempt to give you the science. All matter occupies space (has volume) and has mass. One way we characterize matter is by its density. On the surface of the Earth, the measured weight of an object is its actual weight adjusted for its buoyancy. (Other effects such as variations in Earth's gravitational field, and centrifugal forces are ignored here.) Oil floats on water, fresh water can float on sea water, most woods float on water. Why? It is because their density is less than the fluid they are floating in. A helium balloon will float in air, so will a hot air balloon, for the same reason. It can be confusing to think about things like fluids, gasses, liquids, solids, crystals and molecules. If you take equal volumes of alcohol and water and mix them together, the total volume decreases, but only by a couple of percent. The mass of the two liquids adds up exactly to the total mass (allowing for any spills or losses). Mass is conserved in the everyday world, and volume is often "almost" conserved for liquids and solids. Volume is not at all conserved for gasses.
I hope its no surprize to you to learn that a rock sinks in water. (assuming its density is greater than the water's). Putting that same statement another way, a rock will displace the water and drop. If I were to do the opposite experiment, and pour water into a container holding a rock, I would find that the water does not displace the rock. If I were to do the same experiments with sand, I would find the same thing, that the sand displaces the water and not the other way around. But I might also note that the water "soak in" to the sand. If I were to measure the density of the sand and compare it to the density of quartz (which is the crystalline material most sand is made from) I would find that the sand is a LOT less dense than the quartz. Why? Well, one clue is that when I let water soak in, I might actually be able to see the air bubbling out of the sand. If I did the experiment in the right way, it would be easy to "catch" this. So, sand displaces water, water displaces air. Its all about density. Now, back to your question: "Why doesn't water displace rock and flow to the center of the Earth?" If that is what you meant, then hopefully the answer is obvious, now. But maybe that's not what you meant, instead your question was:"Why doesn't water displace the air in the Earth's Crust and Mantle and Core and flow to the center of the Earth?" Well if you read the Wikipedia article, you'd know that the Mantle and the Core are liquid rock and liquid metal, but perhaps I have to mention that both are much more dense than water? So, that leaves us with the question: "IS there air in the Earth's Crust which can be displaced by (denser) water?" The answer is: Not much, unless its trapped (like water is in a bottle), water will displace it. Meaning there is a lot more water in the Crust than air, and of course a lot more rock there than water.