All of the books in Meyer's Twilight saga have some classical inspiration. Twilight has some Pride and Prejudice elements going on. New Moon is closely tied to Romeo and Juliet. Eclipse pays homage to Wuthering Heights, and Breaking Dawn reflects on two Shakespeare stories, The Merchant of Venice and A Midsummer Night's Dream. Here's what Meyer has to say about the connection between The Merchant of Venice and the last installment of the Twilight series:
I'm not the kind of person who writes a Hamlet ending. If the fight had happened, it would have ended with 90% of the combatants, Cullen and Volturi alike, destroyed… Because I would never finish Bella's story on such a downer – Everybody dies! – I knew that the real battle would be mental. It was a game of maneuvering… Alice tore a page from The Merchant of Venice because the end of Breaking Dawn was going to be somewhat similar: bloodshed appears inevitable, doom approaches, and then the power is reversed and the game is won by some clever verbal strategies; no blood is shed, and the romantic pairings all have a happily ever after. (source)
The Merchant of Venice is a Shakespearean comedy about two Venetian merchants (you might have guessed that piece), Antonio and Bassanio, caught up in a crooked business deal that sparks an unfortunate debt to a moneylender named Shylock. Antonio promises to pay it off with a pound of his own flesh, in case he shouldn't be able to repay it with money. When he fails to get the cash, things look quite bloody for him. But, as in Breaking Dawn, a woman, Portia, saves the day. She's a heiress who has fallen in love with Bassanio. She disguises herself as a lawyer to plead for Antonio's defense before Shylock in court. In a few strategic verbal moves, Portia not only gets Shylock to forfeit everything he owns, but to beg for his life. Shylock leaves, defeated, just like Aro and his whole army do at the end of Breaking Dawn.
As for Breaking Dawn's connection to A Midsummer Night's Dream, Meyer explains:
When I decided to use A Midsummer Night's Dream, it was because I knew that the love triangle that was so painful for everyone involved was going to be flipped around so that everyone was happy. (source)
A reference to A Midsummer Night's Dream appears twice in Breaking Dawn. It's first mentioned in the epigraph to the second book (see "What's Up with the Epigraph?" for more info). The line in the epigraph suggests that love and reason don't go together. That's basically what Bella tries to explain to Jacob in the scene where she tells him that she's convinced things will work out for her and the baby. She senses that some kind of magic fate led her to this point. When Jacob doubts her belief and pretty much tells her she's lost her mind, she appeals to him by saying that once he'll imprint, he'll understand the magic of love:
"Edward told me once what it was like – your imprinting thing. He said it was like A Midsummer Night's Dream, like magic." (10.56)
To put things in context, A Midsummer Night's Dream is a comedy written by Shakespeare. It's partially set in Fairyland and features a lot people falling in and out of love by the power of magic potions. Sometimes magic is used to promote good pairings, other times to make hysterically bad matches (like when the Queen of the Fairies ends up falling for a guy with a donkey head). So Jacob imprinting on Renesmee is kind of like that – instantaneous and magical rather than reasonable. So, in short, A Midsummer Night's Dream stands for the power of love which drives many of the decisions the characters make in Breaking Dawn – even if from an outsider's perspective it looks like they've lost their minds.