A special effects wizard is a wizard that provides the various effects that may be required in a wizarding play. These wizards generally pop up from somewhere off-stage, such as a trapdoor beneath the stage's floor, perform the required spell that has the desired effect, and then exit. An example of a play that requires a special effects wizard is Hélas, Je me suis Transfiguré Les Pieds, in which one is needed to provide yellow smoke to accompany Crapaud's foot-transfiguration.
Though these wizards are presumably supposed to stick with the spells the script says to cast, this is not always the case. In a particularly infamous performance of Hélas, Je me suis Transfiguré Les Pieds, the special effects wizard used the Fire-Making Spell instead of conjuring yellow smoke, hoping the effect would liven up what had been a dull performance thus far. However, this merely had the effect of burning down the theatre and ending the play early.