According to the Oxford Dictionary, it means “a small room, leading to a main one”.
There are two small antechambers in Hogwars mentioned regularly.
One is connected to the Entrance Hall, across from the Great Hall ("a small, empty chamber off the hall"). In this room the new first year students heard from McGonagall about the sorting and then waited nervously before being sorted into their houses at the Welcoming Feast. They were also greated by the ghosts of Hogwarts (PS/SS7).
Harry, Ron and Hermione also used this antechamber in Prisoner of Azkaban. They waited for the Entrance Hall to empty, before visiting Hagrid just before Buckbeak was "executed" (PA16).
All fifth-years gathered in this room beside the Great Hall to wait for the practical part of the OWL's to start (OP31). Students were called in alphabetical order, and they did not return upon finishing their exams.
And finally, this room was used to deposit Voldemort's body after his death in Deathly Hallows (DH36).
Another antechamber mentioned is off the Great Hall beyond the staff table. Here hang portraits of whiches and wizards, including the Fat Lady's friend Violet, a wizened witch and of a wizard with a walrus mustache (GF16). It also has a fire in a fireplace. After being chosen as champions by the Goblet of Fire, Fleur, Krum, Diggory, and Harry met in this room with the officials of the Tournament. They also received the instructions for the first task in the Triwizard Tournament. Finally, the champions met their families here before the third task in the Triwizard Tournament (GF31).
Antechamber derives from the Lating words "Anti" meaning "preceding" and "camera" meaning "vault, arched chamber", according to the Oxford dictionary
The word "antechamber" is only used once in the story, by Dumbledore to describe the entrance hall to the cave in Half-Blood Prince (HBP26). The Hogwarts' antechambers are called small chambers in the books. Looking at the meaning of the word "chamber", this is a bit odd: according to the Oxford Dictionary, chamber means "large room, used for formal or public events". However, in (old) Middle English, it means a "private room". That's more in keeping with the way the small room off the Great Hall is used.
In GF/f the champions were led to the Trophy room in stead of the antechamber.