If a signal depends on only one variable then we call it one dimensional, and if a signal depends on two variable we call it a two dimensional signal.
But when we represent an one dimensional signal, we use two axes(amplitude vs. time). In case of a two dimensional signal, we use two axes (for example, the x axis and the y axis in an image).
How can I understand the difference between a one and two dimensional signal?
Basically the dimensional number refers to the number of independent variables (input).
In one dimensional signal $f(t)$, the amplitude $y=f(t)$ is the dependent variable (output), and there is only one independent variable $t$.
In two dimensional image $f(x,y)$, the two independent variables are $x$ and $y$, and the dependent variable $f$ is also called intensity. If you want to make it similar with amplitude vs time plot as you do with one dimensional signal, you can plot a intensity vs x vs y scattered dots with three axis as well.
x, y represents the image plane and in this case it's 2D plane, or 3D plane. So it's amplitude plane in front of the time plane. Like graphical representation, we could have the simple case as one vector or more than one which consist a plane. So we represent the time plane vs amplitude (perpendicular planes)
