The Gathering Called the ExtraOrdinary Ghosts to the Wizard Tower. It would occur whenever an Apprentice finished the seven-year-and-a-day term and had to Draw for the Queste.
Usually, the Gathering only takes place when an apprentice is about to complete his or her seven year term as an apprentice, but that was only tradition. It was not officially stated as a must. So, in Queste (the book), Tertius Fume starts the Gathering and is able to make Septimus Heap go on the Queste.
During the Gathering
During the Gathering, the ExtraOrdinary Wizard has to step down from his or her place as ExtraOrdinary Wizard, and become "One voice among the many", all as equals. But that can only happen when all the ExtraOrdinary Wizards arrive at the Wizard Tower. A notable exception to this is Hotep-Ra himself who, as he is still living, yet has no ghost. It is notable that now Septimus was the last apprentice to go into the Queste and DomDaniel'ss ghost dissappeared, so it is unknown if there will be any Gatherings in the future.
The Queste was originally a mission made by Hotep-Ra to go to the House of Foryx and meet him. This Apprentice would have to draw a questing stone and must report to Hotep-Ra all the happenings inside the Castle. However, he did not know that Tertius Fume, his once best friend, bewitched the whole Queste by making the Apprentices go onto an Enchanted boat which drains off Magykal powers, and by making the Questing Guards kill the Apprentices. Until Septimus Heap, there has never been an apprentice who has completed the Queste and reached the House of Foryx to meet with Hotep-Ra.
In The Magykal Papers, Alther's Guide to Being Dead's "Advanced Pamphlet" includes information on being Gathered; that is, being Called to the Wizard Tower to participate in a Gathering.