Four dimensions are experimentally supported.
The three space dimensions I assume you're familiar with.
The time dimension is, mathematically, very difficult to distinguish from the space dimensions. All the operations that work with distance and volume etc. work perfectly well when applied to it.
There is a factor of sqrt(-1), however, and I suspect - with no experimental or logical support - this reflects a fundamental difference with the time dimension that means, among other things, that you cannot accelerate or decelerate in the time dimension. Even so, it's still a dimension, just a special one.
If you're not afraid of math:
Basically, every particle can be entirely described by its wavefunction or something like it, which maps a distribution of a value across space and time. The relationship conforms to the strictures of the definition of function. (Hence the name.)
The thing about functions is they can have any number of dependent variables, but they must have one independent variable. I believe time's special properties are the consequences of its status as the physical independent variable.