The significance of "A Midsummer Night's Dream" is perhaps best captured by Lysander:
The course of true love never did run smooth (1.1.132–140).
This line represents the conflict that most of the characters face in the play, from young lovers to fairies to royalty.
Early in the play, Helena finds herself rejected by her love interest (Demetrius), but through the work of the fairies, both he and Lysander fall in love with her. This greatly upsets Hermia, who Lysander had wanted to marry before the fairies' interventions. Hermia and Lysander had originally fled into the forest because Hermia's father and the king, Theseus, had forbidden their marriage. Hermia's father wants her to marry Demetrius instead.
Because she refuses to submit to the will of her husband, Titania is forced to fall in love with Bottom, who has been turned into a man with the head of an ass.
Hippolyta, who was once a strong female warrior, has been "gifted" to Theseus. She has been conquered by her husband, who reminds her that he "won [her] love doing [her] injuries" (1.1.18).
"Love" makes these characters act in unexpected and in often unbecoming ways. Male characters in particular conquer, deceive, abandon, and realign in an effort to achieve "true love." In each of these instances, women in particular are manipulated by the male authorities in their lives, their own will bent to concede to men's overreaching sense of authority.
In this play, we realize that "true love" doesn't run smooth because the voice of women is largely ignored as men try to create a world that dismisses the desires of women. Therefore, although this play ends with a sense of "happily ever after" resolution, the audience is left to ponder the cost of such "happiness." What have women been forced to sacrifice? Why is the manipulation of a woman's feelings (particularly one like Titania who is primarily concerned with the welfare of a child) humorous? Why do men feel the need to physically conquer women, as is seen in both the relationship between Titania and Oberon and the one between Hippolyta and Theseus?
Perhaps "true love" doesn't "run smooth" when it isn't love at all. Instead, this play demonstrates the conflicts that arise when women are forced to concede their own desires to align with the goals of men.