Think of dimensions as the number of pieces of information required to uniquely identify the position of an object.
In 1D, you only need one number.
In 2D, two.
In 3D, three.
But in all these scenarios, the point in question is "static". What if the position of the object was also changing in time?
Then, it wouldn't be sufficient to provide just the spatial coordinates, you'd also need to specify what time it is. In 1D for example: at 12:00 the point was at 0. At 13:00, the point was at 1.0. At 14:00 the point was at 2.0.
Thus, "4D" in special relativity comes from 3 spatial dimensions + time, since we care about how things move through "space and time".
One difference of course is that while we can always return to a physical position in space, even if the contents of that space have changed, it seems very conceptually challenging to imagine returning to a position in time even if the contents of that time had changed. What would this even mean?
Our definition of time seems therefore to be two things: first, a snapshot of physical state (in which we imagine points in time a bit like Back to the Future), and secondly (as other comments have noted) a measure of periodicity.
The latter is that which we seem to be measuring experimentally (e.g. with differences in atomic clocks within gravitational fields). However what we are literally measuring seems to be something like “how many times can a given particle move/irradiate relative to another given particle before we bring them back to each other”. Reducing to a pendulum for example, we could imagine that the space was “more dense” so it took longer to travel the same apparent distance, a bit like how light takes longer to travel through particular materials. Another way to see this would be a kind of universal framerate.
So based on this possibly weak conceptual understanding, I can certainly imagine a fourth property of any given spacetime location that reflects how frequently events can occur in that space (a kind of EM-field view of time), but to consider this as a geometric “position” or coordinate is something I conceptually struggle to imagine.
In 1D, you only need one number.
In 2D, two.
In 3D, three.
But in all these scenarios, the point in question is "static". What if the position of the object was also changing in time?
Then, it wouldn't be sufficient to provide just the spatial coordinates, you'd also need to specify what time it is. In 1D for example: at 12:00 the point was at 0. At 13:00, the point was at 1.0. At 14:00 the point was at 2.0.
Thus, "4D" in special relativity comes from 3 spatial dimensions + time, since we care about how things move through "space and time".