I don't know either. I believe Srini told me once it was based on a USGS (or USACE?) algorithm based on catchment area and perhaps average slopes.
Perhaps it's right on for some parts of the USA, but my experience in Minnesota has been that ArcSWAT channel widths are about 3 times larger than actual, and that when I reduce channel widths (by dividing by 3), flow velocities increase (by 3x) up to about measured values. Channel depths were "about right." I have only a few data points and it would be a worthwhile project to document this more carefully, because it greatly affects channel erosion and sedimentation (and hence the effect of setting the SEDCON and SEDEXP parameters).
My advice would be to use Google Earth to measure actual channel widths at a dozen reaches in your watershed (from downstream up to headwater reaches), and get a dozen actual / ArcSWAT width ratios, and simply use the average ratio to correct the ArcSWAT widths to actual. Do this before sediment calibration (if you allow channel erosion and deposition) for sure, and one would think it would affect the hydrologic calibration as well, since velocities should affect propagation of flood peaks. This might be more significant in affecting the timing of flood peaks in larger watersheds, although I have never heard this discussed in the literature and I'm only speculating here.
Best,
-- Jim