why time moves differently while closer to a massive body?
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This requires a couple of a leaps, but it is the most intuitive explanation.
Space and time are intrinsically connected. Just like up and down are in the same coordinate system as left and right and forward and back, time is part and parcel of that same coordinate system. Here is where the leap comes in: everything is moving through space time at the speed of light. If you are stationary, you are hurling through the time direction at the speed of light. If you are moving through space at the speed of light, you are not experiencing time. The two are intrinsically linked, and that’s what E = mc^2 tells us. There is kinetic energy (mass * acceleration), potential energy, and this intrinsic energy (mc^2) due to this phenomenon. (Side note: E = mc^2 is the special case when kinetic and potential energy are equal to zero.)
If you do some advanced math, you can see that it would take infinite energy to accelerate anything with mass all the way up to speed of light. That is, to exchange all of the mc^2 energy from the time direction into a spatial direction requires more and more energy the closer you get to the speed of light.
The exact mechanism that causes mass is mostly understood, but very complex. A good way to visualize gravity due to mass is that mass creates a type of drag pressure on things that are nearby in space time. Anything that gets close is “attracted” due to this curvature in 4 dimensions.
We still don’t have a full bridge between the quantum world and relativity, so this is where the second leap comes in. The universe of the small behaves probabilistically, whereas the large scale is more classical due to the law of averages. The interactions between particles (gluons, specifically) are actually responsible for the overwhelming majority of mass (>98%) in the universe. It is clear then that particle interactions are somehow causing this warping of space time, but I do not think this is fully understood how this directly interplays with space time.
Many particle physicists want there to be a new force mediating particle dubbed the “graviton”, but that seems to be more fantasy than science. Einstein was hoping that there was some fundamental curvature in space time which would further support relativity, but the universe appears to be frustratingly “flat”. There is still a lot to discover about our universe.
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