A tool which shows areas of a model that are at or below the minimum radius is useful for manufacturing purposes to see what areas of the model can't be machined with a certain cutter radius. Minimum Radius Analysis highlights areas of high and low curvature on the model and is helpful while identifying the minimum tool radius that is necessary to create these parts in subtractive manufacturing.
In the example above, watch how Minimum Radius Analysis highlights the areas of concave curvature. For tool radius of 0, these are all green, but as you increase the tool radius, you can see that some parts are shaded in red, as these have too high curvature to be correctly manufactured by the tool of that radius.
After you click OK in the Minimum Radius Analysis dialog, a Minimum Radius Analysis item in Analysis folder in the browser is created as shown below. It means you can toggle the analysis on and off by clicking the light bulb next to the analysis and you can also edit the analysis by right-clicking it and selecting Edit.