I'm reading about why the Rayleigh-Jeans formula failed to explain blackbody radiation curves. The Rayleigh-Jeans formula: $$ E = kT\left(\frac{8\pi\nu^2}{c^3}\right) $$
I see explanations saying that the part of the equation in parentheses related to the "number of standing waves that are able to fit into a blackbody cavity". But is it really the number of waves or is it the number of "modes" at a given frequency? Or are they the same thing?
Secondly, I know that $kT$ is the amount of energy given to each "mode". Again, does that mean that each wave at $X$ frequency is given $kT$ energy? Or each "mode" is given $kT$ energy?
Any clarification would be great. I know there are other similar questions, but I feel like my question is a little different.