Answer:
As she herself explains, the Fairy Godmother is the embodiment of Cinderella's hope. She did not appear until Cinderella was at her weakest point — in the case of the film, the moment Cinderella nearly loses hope of escaping her abusers and living a better life – and introduced herself as a physical beacon of hope. When her arrival nears, twinkling lights will surround the area in which the Fairy Godmother is to appear; said lights will then gather and form themselves into the godmother.
The Fairy Godmother is equipped with a magic wand that she can summon from nothingness. Said wand holds incredible power, such as metamorphosis and the ability to warp reality, among others. The wand's magic is not exclusive to the Fairy Godmother, however, as mortals can also wield its power and use it as they so please, be it for good or evil. How much magic the Fairy Godmother holds without her wand is questionable, as the only powers she demonstrated without using her wand was her ability to appear from thin air surrounded by sparkles and, as mentioned above, summoning said wand.
Apparently she has a connection with her wand as she was able to find it in Anastasia's hands after losing it in the picnic she made for Cinderella and the Prince, despite the long distance.
Step-by-step explanation: