In sigma-delta modulator's result showing, I often see units defined as
"dB per bin". Sometimes as "dBFs per bin"

How to understand this unit?

Since in sigma delta modulators you deal with noise (quantization noise in this particular case) it is necessary to talk about spectral densities rather than spectra.
Thus dB/bin is a spectral density unit for the noise processed in the sd modulator, pretty much the same way it is done for "continuous time" noise where the PSD in dB/Hz.

In the dB/bin case, you can think of the amount of noise power in each bin, although you cannot tell how it is distributed "inside a bin". That asks for a higher resolution DFT.

Best
Tosei