A magic wand allows a witch or wizard to cast spells, and quickly. Without a wand, spells cannot be cast and at most the witch or wizard may still be able to do potions and use extra qualities. Using the wand that chose your character grants the witch or wizard a +5 to their known spells.
Using a wand that does not belong to you will allow a witch or wizard to still cast spells, but they get no wand bonuses and have to use their base magic roll. After all, the wand chooses the wizard, that much as always been clear.Harry Potter Items