Map generalization guidelines, for instance applicable to CORINE Land Cover or Polish BDOO databases state inclusion criteria for areal features like "area should be > 250 000 m^2 and width should be >125 m". How is such width defined? Obviously for curved areas such as vegetation touching rivers (as in BDOO which treats it as a special condition) one may imagine that simple methods related to geometric axes would break down due to meandering. The fact that these constraints are stated without definition leads me to believe there are established methods of width measurements for polygons, is it so?
I don't believe there is a universal standard. Particular sets of guidelines might explicitly define it, but I haven't seen that done much.
In practice, width tends to be the shorter of the two measurements, length and width. This is only heuristic, of course, but stated more formally, length is the maximum distance across the polygon, border to border, while width is the distance across a polygon, border to border, that lies perpendicular to length. Some might say "height" and width, but I think that's less common because "height" more clearly describes a distance measured vertically.
In the case of this generalization guideline, I think what they're suggesting is that the polygon should be no "thinner" than 125 m. Again being awfully formal for something so heuristic: nowhere in the polygon should an inward-projecting normal on the polygon border be shorter than 125 m before reaching an opposite border.
I imagine this guideline is being given with respect to a certain map scale and drawing resolution. For example, if we imagine a pixel on your monitor is 1 mm wide, or that we can print lines on paper as thin as 1 mm, than the smallest mark we make on the map covers a certain area which will be a function of this 1 mm constant and the map scale. In the case of 1mm in our example, such a mark is 125 m wide at 1:125,000:
125 m / x = 0.001 m
125,000 = x
More likely this 125 m minimum is for a larger map scale, something like 1:50,000 perhaps, to allow room to show two borders and a fill for some map feature at least 125 m wide.