What exactly is the frequency of light counting? Light (as all electromagnetic radiation) has specific frequencies. So taking part of the visible spectrum (say 300THz) then what exactly is happening 300 trillion times every second?
Is it as simple as there is an actual wave, with a wavelength and therefore a frequency, or is the wave a side effect or a mathematical representation of something more fundamental?
 A: Light was identified with electromagnetic waves, when Maxwell combined what the physics community knew as magnetic and electric fields, the data  fitted with various laws,


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.

You ask:

Is it as simple as there is an actual wave, with a wavelength and therefore a frequency, or is the wave a side effect or a mathematical representation of something more fundamental?

At the level of classical physics , if you want to call mathematical formulations "imagination" as in the image above, the answer is that the mathematical representation as waves of varying electric and magnetic fields fits the data.
There is the more fundamental aspect of light which could not be explained by Maxwell's equations, the quantization of light. The classical light is built up by very many photons of energy $h*ν$   where $ν$ is the classical frequency of light. The photons are quantum  mechanical particles of the standard model of particle physics.   Quantum field theory is necessary to understand how this happens, it is not a simple addition but a quantum mechanical superposition of photons. This experiment single photons at a time shows how the interference of classical light emerges from the addition of individual photons.
A: You are correct, there is an actual wave and the frequency is the number of wavefront passing a fixed point per unit time. The waves are waves in the electric and magnetic fields.
When we talk about photons as particles of light this is the quatum mechanical description where all particles in actuallity have both wave and particle like properties.
