We see the supernatural in A Midsummer Night's Dream portrayed through the activity of gods, such as Cupid, through magic, and through fairies. The supernatural serves to join the flawed mortal world with the dreamlike state of the ideal world.
We learn in the play that a certain flower has been given magical powers because Cupid shot an arrow that missed aim and landed in the flower (II.i.168-171). Oberon and Puck decide to use the flower to alter individuals' states of mind into believing that they are in love with the first thing they see. This magical, supernatural act of deception did not at first create any sort of ideal state. Instead, it created chaos by making two men fall in love with Helena and potentially destroying her friendship with Hermia. However, once things have been righted, Lysander is properly coupled with Hermia while Demetrius is rightfully coupled with Helena, whom he was engaged to before he began pursuing Hermia. The rightful pairing of the lovers puts an end to a great deal of grief and sorrow for all members of the couple, especially poor Helena who had been cheated by Demetrius. Because the supernatural, or magic, used created an ideal, peaceful state of love and unity for all of the couples involved, we can say that the supernatural served to link flawed humanity to the dreamlike state of the ideal world.
We know the supernatural created a dreamlike state for the lovers because when they awoke, they felt like they were still in a dream. We especially see the characters confuse reality with a dream when they are found in the woods by Theseus and Egeus and still feel that they are dreaming. Demetrius phrases their state of mind best when he asks:
Are you sure
That we are awake? It seems to me
That yet we sleep, we dream. (IV.i.195-197)
Hence, since the happily united lovers feel that their reality is a dream, we can say that supernatural functions in the play to unite flawed humanity with the ideal, which is seen in a dreamlike state.