It can be used for pretty much anything.Modulation, substitutions,, passing chord, maybe it just sounds pretty, you name it.
+1 @ rAch4Everand like R4e mentioned, very handy as for either outright modulation or temporary forays into false modulation territory, in minor mode, it very much works as a V of V, which allows a piece in c minor to move into key of b flat major with almost seamlessly.
Thanks for the reply, but can you or someone else on this forum please provide some examples of these? -- it would be much clearer to me that way. What is false modulation? It is not obvious to me how the iii/III can be used as a substitution, or as a passing chord. What would the iii/III substitute for?Also, you can modulate from the iii/III chord, using it as a V of V chord, but how do you reach the chord in the first place?