"I remember every wand I've ever sold, Mr. Potter. Every single wand. It so happens that the phoenix whose tail feather is in your wand, gave another feather -- just one other. It is very curious indeed that you should be destined for this wand when its brother why, its brother gave you that scar."
-- Mr. Ollivander (PS5)
"My wand's feather came from Fawkes?"
-- Harry and Dumbledore (GF36)
Phoenix feathers are used in wand cores. Both Harry’s holly wand and Voldemort’s yew wand contained feathers given by Fawkes the phoenix.
The phoenix is a magical bird about the size of a swan. The phoenix has crimson feathers on its body and a golden tail as long as a peacock's. Its claws and beak are gleaming gold and its eyes are black. (These colors happen to be the colors of Gryffindor House, interestingly enough.) The scarlet body feathers glow faintly in darkness, while the golden tail feathers are hot to the touch (FB, CS17).
Phoenix tail-feathers are a powerful magical substance according to Mr. Ollivander, and are suitable for use as wand cores, but are the rarest type (PS5, Pm). Ollivander noted they "show the most initiative, sometimes acting of their own accord, a quality that many witches and wizards dislike ..." (Pm)
Mr. Ollivander had Harry try another wand: "Maple and phoenix feather. Seven inches. Quite whippy" (PS5), but then took it away from him. The core feather must have come from a different bird since Fawkes only gave two for the holly and yew wands.
When two wands are forced to duel that have core material from the same single creature, the result will be "Priori Incantatem," a display in sequence of the last spells one of the wands cast. Which wand will show the spell effect depends on the willpower of the two wizards involved (GF34, GF36)
Ghost figures of some of those murdered by Voldemort's wand emerged from Harry's wand in reverse order to surround him protectively in the "golden web" created by the Priori Incantatem: Cedric Diggory, Frank Bryce, Bertha Jorkins, Lily Potter, and lastly, James Potter (GF34).
Mr. Ollivander told Voldemort that he could avoid Priori Incantatem by using a different wand without a phoenix-feather core, so he took Lucius Malfoy's elm wand. However, because Harry's holly wand absorbed some essence of Voldemort's power during Priori Incantatem, it blew up the elm wand during the Battle of the Seven Potters (DH4, DH5, DH24,DH35)