The Wizard Robe is a specific robe given to students of Bufo.
The wizard robe is floor-length, maroon, purple or brown in color, and has a large hood. Yellow stars automatically appear on it when the wearer accomplishes a trial given to them by Bufo. The amount of stars on a robe is indicative of the wearer's set of magical skills. An Ultimate Wizard, the highest rank of wizard, receives a single large star on the chest that replaces all the previous stars earned. Any level below that has small stars that eventually cover the entirety of the robe.
Bufo's robe is purple in color, and has a single large star on it, indicating that he is an Ultimate Wizard.
In "Wizard," one star is added to the robe for each task Finn and Jake accomplish, and for each star earned, they can perform a new magic spell. When a task is carried out correctly, a small, sparkly gold beam of light shines on the spot where a star soon appears. It has been confirmed that the magic is stored in the robe, since Finn and Jake's robes were destroyed at the end of the episode, and they haven't used magic since.
The known magic powers used by Finn and Jake throughout "Wizard" include: Dragon Eyes, Tiger Claw, Vorpal Hand, Blazing Feet, Beauteous Wings, the ability to instantly create facial hair, Dustomancy (mastery over all dust motes and the ability to read their emotions), Shadowcery (ability to control shadows), the ability to shoot fireworks out of one's finger, the ability to shoot a "limitless supply" of mayonnaise out of one's finger, and the ability to cast sleeping spells.