Though they are not commanders, they are subject to Duty to at least some degree. Their ruler can give them the authority of a Chief of Staff in charge of at least Casters and other courtiers. Though it's unknown if this authority/rank has the same ability to issue orders that a Chief Warlord or Chief Caster enjoys.
There seem to be many subtypes and roles for courtiers. Jesters traditionally act the fool at court, use Rhymeomancy to create satyrical songs, and juggle or perform other acts to entertain their ruler and other members of the court and visitors. Manservants and maids serve tea, help higher ranking units dress, clean personal apartments, and serve food. Scribes and record keepers maintain documentation about things like crop yields and finances. There may be other subtypes that are as yet unseen.
Royal sides like Jetstone use courtiers to deliberate matters that affect the side, even developing sophisticated rules to discuss and decide proposals to take to their ruler for approval. Jetsone has also developed a courtly culture where warlords can fall into and out of favor, leading to things like being traded to another side or made to manage a city. Such were the fates of Topotato and Duchess Artemis, respectively. Courtiers in Follywood filled the court with intrigue and plots, leading to some occasionally falling so far out of favor as to be disbanded.
Courtiers do not appear to be necessary to run a side, and in fact there are sides like Gobwin Knob and Transylvito that do not use courtiers at all (albeit this is considered a risky extravagance). In the case of Transylvito it's because Don King thought them untrustworthy and trappings of nobility, and arranged to have what few courtiers he inherited from his father moved to outlying cities or diplomatic errands until all were croaked or turned. It's unknown why Stanley doesn't use courtiers, though it may be partly due to his disdain for nobles. Some sides, notably Homekey, use a small number of courtiers as subject experts expected to advise on a wide range of matters and even offer military advice.
These are some of the roles or functions Courtiers have been seen to do.
Courtiers may be able to manage cities in place of warlords. Don King's observation that using warlords instead of courtiers was "a risky extravagance" suggests that courtiers may be significantly cheaper to pop and have lower upkeep than Warlords who are more useful directing battles in the field. It is possible that Warlords provide a larger efficiency boost to their city than a courtier (to make up for the higher expense) but may have questionable strategic valueErf-b1.5-p035 when the city is not under siege.
In this way they may act as a sort of friendly "A.I."; in some strategy games, the computer can handle basic maintenance for you.
Courtiers have only been mentioned in reference to Royal sides. Whether this is a coincidence or a benefit of Royalty has yet to be seen.
Before book 2, everyone in Erfworld was a combatant; no one even had a concept for "civilians" as Parson understood it. Being non-combatants means courtiers may be the closest Erfworld has to civilians.