A Greek chorus in the modern sense is a small group of characters who are not really part of the story in a work of fiction, but more observers of the story. This slightly outside perspective allows them to comment on the story, either by providing a sort of narration, or by providing critiques and commentary.
The term arises from the use of a chorus in Ancient Greek plays, who performed a similar role, often with the addition of singing and dancing.
In Star Wars, C-3PO and R2-D2 sometimes act a bit like a Greek chorus, commenting from the sidelines on the actions of the other characters, but at other times they act like traditional characters important to the story. In The Muppet Show Statler and Waldorf pretty much are a Greek chorus all the time, although their commentary is mostly just heckling.
To bring this back to gaming, you can try adding a Greek chorus to a roleplaying game. They would be NPCs who have some reason to tag along with the PCs. It doesn't have to be a great reason. If the adventure is mostly a city-based one, have a couple of comical gargoyles who always seem to be sitting on a rooftop edge nearby when a scene happens, making comments on the combat or the heroes bargaining attempts or whatever. In the countryside, have a couple of kids follow the heroes around like, well, heroes. You could also use a pair of spellcasters' familiars as a Greek chorus.
Besides providing commentary, such a Greek chorus can act as a sort of mouthpiece for the GM, providing an in-character way of dropping hints and comments like "Oh, I'm not sure I'd try opening that suspiciously demonic looking book... but, you know, whatever floats your boat."
Kermit: You want another one?
Theatre Audience: Er... maaaybe?
Kermit: Do you want another one?
Theatre Audience: Is it better than the last one?
Statler: It matters not whether we want another one. In the battle of the wills, desire is the root of all suffering.
Kermit: Do you want another one?!
Theatre Audience: Nooooo!
Fozzie: Let's give it to them anyway!
Kermit: You want another one?!!
Kermit: Let's rip it up!!!
Waldorf: I wish we'd ripped up these tickets...