Magic wand is a common name for a device that allows people cast spells they don't have. The technical name for them is "spell catalyst". Spell catalyst doesn't need to be in shape of the wand: Tedd's magic watches are an example of such.
While magic wands can allow normal people to cast spells, to the point where Edward Verres can use fireball wands as an example of the dangers of widespread public knowledge about magic, they are usually used by other magic users. Only wizards can learn other people's spells, so if a non-wizard magic user needs one or more specific spells they don't have, or if a group like DGB needs standard issue spells for every agent, they need to use wands with preset spells.
In addition to letting someone cast spells, spell catalysts can usually store energy so the user doesn't need to use as much of their own energy to casting. The capacity of a catalyst depends on size, material and crafting quality. Tedd's watches are an exception to this, as they don't have any storage capacity, relying on the caster's energy and, while in Moperville, the ambient energy buildup.