The main thing that I’ve used it for is testing DC offset removal 
Adding offset is not something that one would be likely to use musically very often, though it could perhaps find use in synthesis or sampling. I think that it’s more likely to be used with non-audio signal processing (Audacity finds lots of weird and wonderful uses in classrooms).
There’s not much in the way of “documentation” for it as yet, though there is quite a lot of information about it in these two topics:
The tool was really developed as a tool for studying DC offset and experimenting with ways of removing it.
In brief,:
“Dynamic” compensates for offset using a “rolling average”, which enables it to cope with an offset that changes slowly over time.
“Absolute” is the method used in the Audacity Normalize effect.
“HP Filter” is a High-pass filter (as used in the LADSPA DC offset removal plug-in).
“Abs + Filter” is the above two, one after the other.
“Equal +/- Peaks” is not actually “offset removal”, but centres the waveform according to the maximum positive and negative peaks.
“How much to add” has a range of +/- 1 (as it says in the interface) and is the same scale as the default vertical scale of a wave track.
I would expect a practical “bias compensation” tool would have a much more simple interface, and would probably be for bias removal only. I’d like the default setting to be an “auto” setting, where the plug-in just does it for you, using the most appropriate method for the material.