Symbolically, night and the forest are seen as times and places of liminality: that is, they are between the realms of the living and the dead. The first responder is correct that there used to be a strong belief in fairies in old England; and fairies are also believed to dwell in liminal places, hence their homes in folklore being described as beneath hollow hills or deep in the forest.
In a place or time of liminality, characters may be released from the bonds of propriety and the demands of the mundane world. By behaving in ways they normally would not, they can reveal their dfeepest feelings and motivations. Because the relationships in A Midsummer Night's Dream are beset with misunderstandings, it makes dramatic sense for them to be addressed with trickery, so that the characters' extreme behavior can express their innermost desires. The "magic" performed by the fairies also allows the human lovers to see their problems in a new light. Everyone is transformed on this magical night.