A colour illustration by Clarence F. Underwood for the novel Beau Brocade by The Baroness Orczy.
I came upon a brief but interesting discussion at Fangs, Fur and Fey about tertiary characters.
Please note that, by and large, the following quotes or paraphrases a number of the points raised.
One writer neatly summarized the role of tertiary characters as (1) those who help -- or obstruct -- the protagonist, (2) those that symbolize some element of conflict or conundrum, and (3) those that provide a useful revelation about the protagonist's character/actions/motivations.
One could be finicky and mention that there is really a fourth type of character with which we populate our novels, those sometimes rendered en masse (crowds, mobs, hordes, throngs, packs, hosts, troops and such), sometimes as a singular and equally anonymous wandering walk-on -- those types whose main purpose is to provide local colour, texture, and background to a scene, lest the stage seem unrealistically empty and bare.
Even so, one writer suggested these nameless backgrounders can provide added value beyond just stage dressing, not only to trigger a reminder, an observation or a conclusion from the main character, but also to insert some necessary prop in the story line.
Double duty - always our job.