One of the roles of the supernatural in A Midsummer Night's Dream is to create a dreamlike state that helps portray Shakespeare's theme of fantasy vs. reality.
Critic Northrop Frye points out that in Shakespeare's time May 1st was believed to be "a spooky time" when both "benevolent and malignant" spirits came out ("Mythological Background"). We know that the play begins on the eve of May 1st and ends on May Day because, when Theseus finds the four lovers asleep in the woods, he remarks that they must have awoken in the woods in observation of May Day, which was celebrated with sunrise singing, as we see in Theseus's lines:
No doubt they rose up early to observe The rite of May; and, hearing our intent,
Came here to grace our solemnity. (IV.i.132-134)
Hence, it makes sense that during their night in the woods, the lovers encountered spirits and experienced some spooky enchantment. The enchantment the lovers experience creates a dreamlike state, showing us that one of the roles of the supernatural is to create a dreamlike state in honor of the First of May and which also helps to portray Shakespeare's theme of fantasy vs. reality.
The fairies create a dreamlike state by manipulating the minds of the lovers. Before they go into the woods, both men are pursuing Hermia; now that they are in the woods and enchanted by Puck through the magic flower, both men are now pursuing Helena. For the lovers, the dreamlike state is one of madness, especially for both women. Helena disbelieves the sincerity of Lysander and Demetrius, believing that they are actually mocking her. Helena then begins to believe that even Hermia is in on the joke, as we see in Helena's line, "Lo, she is one of this confederacy!" (III.ii.195). The dreamlike state is actually a nightmare for Helena because now she believes that Hermia has intentionally severed their life-long friendship that began in childhood. Likewise, the dreamlike state is a nightmare for Hermia, because she has now lost the true love she has endangered her life to elope with. However, the story is resolved at the end, giving the "dream" the lovers experience a happy ending. Hence, we see that the role of the supernatural is to create a dreamlike state that is actually also a bit spooky and nightmarish, portraying Shakespeare's theme of fantasy vs. reality.