What is the $y$-axis in an electromagnetic wave? Apologies if my question is unclear, any help to clarify it along the way is most welcome.
I'm confused about what we mean when we say electromagnetic 'waves' (say visible light). In the usual mental picture we have of a simple sine wave, what does the y-axis correspond to? In mechanical waves like water or sound, we can plot the vertical displacement of each particle along the x-axis as a value on the y-axis. Alternatively we can fix a specific particle in the water/air and take the x-axis to be time and the y-axis to be its physical displacement.
But for light traveling in a vacuum, there would be no such displacement of particles. So what does the y-axis correspond to? What do we mean by light being/behaving like a wave?
 A: Of course what is reported onto the $y$-axis is a matter of arbitrary definition. But usually the standard way to depict an electromagnetic wave is to report onto one of the three orthogonal axis the strength of the electric field, on another one the strength of the magnetic field, and the last third axis is taken to be the axe of propagation of the electromagnetic wave.1
Keep in mind that this depiction of an electromagnetic wave is not an abstraction without connection to reality: is not simply a way to represent the wave that we have choosen arbitrarily: in fact it can be proven that the two fields, electric and magnetic, in an electromagnetic wave, are always ortogonal to each other and orthogonal to the direction of propagation of the wave; this follows directly form the Maxwell's laws, that lead to the wave equation.

[1]: With the word "strength" in this context we mean the module of the electric or magnetic field vector in that point in space.
A: Maybe this will help


Electromagnetic waves can be imagined as a self-propagating transverse oscillating wave of electric and magnetic fields. This 3D animation shows a plane linearly polarized wave propagating from left to right. The electric and magnetic fields in such a wave are in-phase with each other, reaching minima and maxima together.

Here y is the axis of propagation of the wave.  Because of polarization x,z are the axis where the electric and magnetic field amplitude changing with time is expressed for each point on the y axis. In diagrams the y axis could be considered an optical  ray.
