A phoenix feather is a tail feather from a Phoenix. The feathers given by Fawkes were noted for their striking scarlet color, consistent with his plumage. When used as a wand core, a single feather is placed at the center of the wand's wood. Harry Potter's wand is described as containing one such feather.
Phoenix feather is one of the three “Supreme Cores” used by the renowned wandmaker Garrick Ollivander, alongside dragon heartstring and unicorn hair. It is considered an exceptionally powerful and rare wand core.
The most significant phoenix feathers in wizarding history were the two given by Albus Dumbledore's phoenix, Fawkes. The master wandmaker Garrick Ollivander procured these feathers and used them to craft two individual wands. The first wand, made of yew, was thirteen-and-a-half inches long. It was sold to a young Tom Riddle, who would later become Lord Voldemort. Decades later, the second wand, made of holly and eleven inches long, was presented to Harry Potter at Ollivanders in Diagon Alley. The wand “chose” Harry, a decision Ollivander found very curious, as its brother wand had been the one to give Harry his lightning-bolt scar. This shared core bound the two nemeses together long before either of them understood the connection's full significance.
The phoenix feather core is central to the connection between Harry Potter and Lord Voldemort, serving as a physical manifestation of their shared destiny.