Tweet of the Day: Walking the Walk
This is a world building trope if there ever was one. The nature of the Magical Society, an organization that brings together those who can wield magic in a given setting, is a reflection of the setting as a whole. A secret society of mages exist in a world where anonymity is the best protection for those who use magic from those who don’t. In another setting magic might exist in public, but still regarded as dangerous so the magical society serves to enforce regulations about its improper use. Still others are more like medieval guilds or modern unions, that represent the social/political/economic interest of its members. Many a mage guild in tabletop fantasy games fits this description.
Real life magical societies sprung up in the 19th and 2oth centuries, such as the Golden Dawn. Societies like this acted like informal social clubs with religious undertones rather regulatory bodies. Your world can also have a mix of these, each reflecting an aspect of magic and its impact on society.