Wand Cores and Woods: What Your Wand Says About You
The three cores
The three wand cores used by Ollivander, the wandmaker the books focus on, are phoenix feather, dragon heartstring and unicorn hair. Each has different qualities, and the books imply that the core chooses the wizard as much as the wizard chooses the wand.
Phoenix feather wands are the rarest and the hardest to win the loyalty of. They're capable of the widest range of magic but can sometimes act on their own. Harry's wand and Voldemort's wand both have phoenix feather cores, from the same phoenix, which is the connection that drives several key plot points.
Dragon heartstring wands are the most powerful and the quickest to learn new spells, but they're also the most likely to turn to the Dark Arts if the wizard is inclined that way. Hermione's wand has a dragon heartstring core.
Unicorn hair wands are the most consistent and the least likely to fluctuate or be used for dark magic, but they can be prone to melancholy if seriously mishandled. Ron's first wand, a hand-me-down from his brother Charlie, had a unicorn hair core.
The woods
Wand woods are more varied and more personal. Holly, Harry's wood, is traditionally associated with protection and is said to choose owners who are engaged in dangerous or spiritual quests. Vine, Hermione's wood, is drawn to witches and wizards who seek a greater purpose and are sometimes surprised by the direction their magic takes them.
The most interesting lore detail is that elder wood wands, the rarest of all, are supposed to be deeply unlucky. The Elder Wand, the most powerful wand ever made, confirms this: every one of its owners dies violently, until Harry breaks the cycle.
Pottermore, now Wizarding World, expanded the wand wood descriptions significantly, giving each wood a personality profile. Fans have spent years matching these to characters and to themselves.
What the wand lore is really about
The wand system is one of the cleverest pieces of worldbuilding in the series, because it works as both a plot device and a personality test. The idea that the wand chooses the wizard is a way of saying that your tools reflect who you are, not who you want to be.
This matters most at the end of the series, when the allegiance of wands becomes a plot point. The Elder Wand doesn't follow power; it follows the person who won the loyalty of its previous owner, even by something as small as disarming them. The message is that mastery comes from relationship, not force, which is the theme of the whole story.