Why do wand materials and lengths matter?
The spells that a wand can perform are affected by the type of wood used, the wand's flexibility, length, and the core. For example, longer wands work well with taller witches and wizards and are best suited to bold personalities, whereas shorter wands are better at performing elegant magic.
Ollivander's wand shop in Diagon Alley sells only three wand cores they believe to be of the best quality, each of which has its own personality. Unicorn cores are loyal to their owners and are the hardest wands to turn towards the Dark Arts. Dragon heartstrings are the most powerful but are easily won over by potential new owners. Harry Potter's wand contains a phoenix core, the rarest and most independent wand core – they are picky and won't take just anyone as their owner. Phoenix cores can also take a little while to reveal their magical abilities.