All the diagrams showing how massive bodies warp the space/time continuum (causing what we consider gravity) show the continuum as a 2-dimensional graph. Why is it planar and not 3-dimensional?
Space time is four dimensional.
Space time has four dimensions. It has three spatial dimensions and the fourth dimension is time. The problem is that we live in a three dimensional world from the point of view of our senses. We can't visualise four dimensions.
So, to give an analogy of what curved space time looks like we reduce the number of spatial dimensions to two so that we can visualise it.
So, in the diagrams, the horizontal surface represents two dimensions of space. The vertical axis represents the time dimension. Think of it as the more space is stretched down into the time dimension, the slower time passes.