I'm not sure which specific story Gandalf is telling as there are many in the Tolkien's works. Maybe it's about the history of Middle - earth, like the battles against the dark forces or the tales of the rings.
Well, Gandalf is from the Ainur. He was among those Maiar who were sent to Middle - earth. His purpose was mainly to help the good against the forces of evil like Sauron. He was created long before the events in Middle - earth started to unfold. Gandalf's origin story is deeply intertwined with the greater cosmology of Tolkien's world. He had powers that were both magical and related to his wisdom and knowledge, which he used to influence the course of events in Middle - earth.
Gandalf originated from a higher spiritual plane. He was dispatched to Middle-earth with a purpose. His background involves being part of a divine order and having a responsibility to bring hope and resistance against evil.
One of the great stories related to Gandalf is his role in 'The Lord of the Rings'. He guided Frodo on his journey to destroy the One Ring. He used his magic and wisdom to protect the Fellowship from various perils. For example, in Moria, he fought the Balrog to buy time for the others to escape.
Since it's not a part of the original Tolkien concept, it might be a fan - made idea. Fans sometimes like to create alternate versions of characters, and perhaps someone thought it would be interesting to have a 'dark' Gandalf.
There is no "Gandalf the Black" in the original Tolkien lore. Gandalf is known as Gandalf the Grey, and later Gandalf the White. So, there's no story for this non - existent character as such.
One idea could be that Gandalf somehow gets transported to the Harry Potter universe. He could become a mentor to Harry, using his vast magical knowledge and wisdom from Middle - earth. Maybe he helps Harry understand some ancient magic that even Dumbledore wasn't fully aware of.
Gandalf is a Maia. He was sent to Middle - earth by the Valar. He was one of the Istari, a group of wizards. His purpose was to guide and oppose the rising power of Sauron.