Puck is the mischievous sprite who serves Oberon, the Fairy King.
In Elizabethan folklore, Puck (a.k.a. Robin Goodfellow) is a household sprite who, depending on his mood, plays annoying tricks on people or helps them out with their chores. This explains why Shakespeare's Puck brags to us about all the times he's been a pest to local villagers by sabotaging vats of ale and ruining the batches of butter that housewives spent all morning churning.
Puck loves a good practical joke more than anything else. After transforming Bottom's head into that of an "ass," he gleefully declares "My mistress with a monster is in love" (3.2.6). Because of his fun-loving spirit and willingness to prank anyone and everyone, he's often considered the heart and soul of the play. His antics and his sense of humor inject A Midsummer Night's Dream with a playful and topsy-turvy spirit that creates much of the play's fun atmosphere. It's no wonder that literary critic Marjorie Garber describes Puck as the "principal actor and agent" in a "world of enchantment, magic, music, and mischief."
If Puck creates the play's fun and rowdy atmosphere, then he's also the character who makes things happen in the play. He whizzes around the globe (in forty minutes no less) to fetch Oberon's magic love juice (2.1), and when he accidentally squeezes it in Lysander's eyes (2.2), he sets in motion all the comical misunderstandings that arise from the young lovers' chase through the woods.
After turning the young lovers' worlds upside-down, Puck is also the figure who helps restore order and sets things right. By giving the young lovers the antidote (OK, not Demetrius) to the love juice (3.2), Puck removes the obstacles they've faced and ensures the play's happy ending. According to scholar Stephen Greenblatt, this aligns Puck with the Latin comedies of Terence and Plautus, which feature a "crafty slave" figure. Greenblatt tells us that this "stock character [...] sometimes seems to enjoy and contribute to the plot's tangles but [also] manages to remove the obstacles that stand in the way of the young lovers."
We also want to say that Puck embodies the play's theme of "Transformation." He famously transforms Bottom's head into that of a donkey, and he's also fond of shape-shifting himself. At one point, he brags that he often pretends to be a stool and then disappears so that old ladies will land on their "bum[s]" (2.1). He also terrorizes the Mechanicals in the woods after turning their friend into a human-donkey hybrid:
Sometime a horse I'll be, sometime a hound,
A hog, a headless bear, sometime a fire,
And neigh, and bark, and grunt, and roar, and burn,
Like horse, hound, hog, bear, fire, at every turn. (3.1.110-113)
Puck's ability to transform himself isn't limited to shape-shifting. He can also change his voice, as when he leads Lysander and Demetrius around the wood by mimicking their voices and calling out to each of them.
In some ways, Puck parallels Philostrate's position as Theseus's "Master of Revels." (In Elizabethan England, the Master of the Revels was an important guy in charge of all the entertainment at court—basically a royal party planner. Eventually, the position involved determining which plays could be performed on public stages.) Think about it. Philostrate's job is to make sure Theseus and his court are entertained. This is why Theseus orders him to "Stir up the Athenian youth to merriments" (1.1.13). Later, Theseus turns to Philostrate for his entertaining options:
Say, what abridgement have you for this evening,
What masque, what music? How shall we beguile
The lazy time if not with some delight? (5.1.43-45)
Even though Puck may not go around organizing plays and planning parties like Philostrate, his main function as Oberon's go-to guy is to entertain the Fairy King. As Puck says, his duty is to "jest to Oberon and make him smile" (2.1.46).
By setting in motion the events that send the lovers into chaos, Puck also ensures that we, the audience, have a good time as well. In this way, Puck is also a kind of "lord of misrule" figure (one who was appointed to reign over carnival festivities, which included drinking, eating, and raucous theatrical productions). It's fitting, then, that Puck should close the play by delivering the Epilogue. He is also the only character with the credibility to tell the audience that he knows the play is unreal, like a "dream," and he promises that, if we didn't like the play, he'll soon make it up to us with another one.