In A Midsummer Night's Dream, how do the plot and the characters have a connection?

Shakespeare, of course, was not generally a creator of original narratives - his plays were usually adapted from existing sources, and the core of his genius lay in the creation of profoundly original, textured, and multifaceted character psychologies expressed and sculpted through their unique voices and imaginative use of language. A Midsummer Night's Dream is one of only two known plays by Shakespeare - along with The Tempest, another magical, dreamlike romp - not to be narratively adapted from any identifiable source. So that in itself is one kind of answer to your question: this is one of the few plays in which the plot and characterization are both Shakespearean originals.

But I think it's more telling to observe that A Midsummer Night's Dream is one of many of Shakespeare plays which toy with the question of what exactly "plot" is. It explores the idea that what we call a story is the result of the interaction between human beings' attempts to work their will and desires on the world, and forces beyond our control or understanding. This very broad theme is reflected across many of his masterpieces, and in several of them, including this one, he uses supernatural powers and characters to embody the power of the artist or playwright to dictate his characters' destinies: the ghost in Hamlet, the witches in Macbeth, the sorcerer Prospero and his spirit Ariel in The Tempest, even the fiendish Iago in Othello, who is not supernatural but who verbally invokes the powers of hell as he goes about his wicked task. The "plots" of all these plays are in a sense created by these forces. In the Dream, this role is filled by the fairies; Oberon is in a sense the callous playwright or director who looms over and assesses the action from a distance, while Puck embodies the active, busy, striving part of the artist's creative consciousness (a lot like Prospero and Ariel, respectively). In this case, the "actors" in Oberon's plot are all those embroiled in his schemes, including Hermia, Lysander, Helena, Demetrius, Titania, and Bottom. What happens to them forms a kind of play within the play (and also, by analogy, a dream within a dream), which is mirrored by the literal play staged by Bottom, Quince, and their companions before the duke. (Unlike A Midsummer Night's Dream itself, this play is based on an existing source, the story of Pyramus and Thisbe taken from Metamorphoses by the ancient Roman poet Ovid.) But like most creative endeavors, both Oberon's project and that of Bottom and company prove to be much more chaotic than their creators intended.

The relationship between plot and character in any major Shakespeare play is a complex issue, and the Dream is an especially complex play, so I hope this brief discussion of my thoughts on the subject will prove helpful to you.