This description is taken from the official wiki of the animated series "the owl house"
A coven is made up of witches that specialize in a specific form of magical abilities. A coven membership is mandatory, and failure to join a coven is a high order criminal offense, potentially resulting in petrification. It is known that people who fail to join a coven have reportedly gone missing. It is also possible for a witch to be bound forcibly to a coven without their consent.
Young witches are encouraged to study under one of the main nine magic tracks in preparation for coven membership, and annually-held "coventions" allow them to explore the various covens before making their choice. There are more than nine covens in total, and if one of the main nine is not to one's liking, there are more to choose from. Most witches join a coven when they graduate from school (usually around 17-18 years of age), though exceptionally talented witches can leave school and join a coven early.
The Coven System is a system for categorizing magic into specific disciplines instituted by Emperor Belos. There are nine main covens, with hundreds of other covens beneath them. The educational system trains young witches along scholastic tracks that prepare them for membership in their chosen coven. Each coven and their respective track has an identifying color and sigil associated with it, and each led by a "Head Witch". Ultimately, covens serve an integral purpose for the Day of Unity.
When a witch joins a coven, their arm is branded with the coven's sigil, and all of their magic is sealed off except the magic of their chosen coven. While a witch will be unable to perform magic outside their specialty, they will still be able to perform general spells such as levitation magic, albeit with greater difficulty. Some covens are more highly-regarded than others, and the highest-ranking coven in the Coven System is the Emperor's Coven, the only coven whose members are allowed to use all kinds of magic.
The brands have a secondary effect. In addition to stopping a witch from performing magic outside their chosen coven, the brands can encase the witch in branch like tendrils and place them in a form of stasis. The brands also serve a function for the Day of Unity, acting as a means to drain magic from witches and transfer it into the nine coven heads.
Each of the nine covens is led by a powerful witch known as a "Coven Head" or "Head Witch", who excelled at one of the nine main types of magic. These respective witches studied at one of the most prestigious magic schools such as Glandus High, St. Epiderm, and Hexside School of Magic and Demonics. Each of the leaders of the main nine covens possesses a medallion of their coven's color with their coven symbol on the front. They are responsible for recruiting new members into their respective covens and play an integral (though currently unknown) role in Emperor Belos's Day of Unity. The main nine covens each have a respective relic on display in the Relic Room within the castle belonging to Emperor Belos.