What is a frequency bin?
It's simpler than you think. When we discretize frequencies, we get frequency bins. So, when you discretize your Fourier Transform: $$e^{-j\omega} \rightarrow e^{-j{2\pi k}/{N}}$$ Our continuous frequencies become $N$ discrete bins.

This is exactly why the following is true: $$n^{th}bin = n*\dfrac{sampleFreq}{num(DFT points)}$$ Note that the FFT represents frequencies 0 to sampleFreq Hz.