What can we learn from A Midsummer Night's Dream?

This play seems to celebrate the power of imagination to alleviate the human errors that come from misuse of power. At the beginning of the play, everyone seems to be chafing under the constraints and failures that come from abuse of power. Hermia doesn't want to marry Demetrius and resents her father's intrusion, while Egeus resents Hermia resisting him. Theseus and Hippolyta seem destined for an unhappy marriage due to his military conquest of her. Oberon and Titania are at war over the changeling boy and create havoc in the natural world. Bottom is too ego-driven to allow the mechanicals' play to acknowledge others' gifts. The magic of theater, that links the lunatic, the poet, and the lover, provides a dream-like vision that makes impossible events possible.
The magic of this play is that everyone is eventually humbled during the night in the forest, and this humility allows the love relationships to sort themselves out more acceptably. The play tells us, "Lord, what fools these mortals be," and that "love looks not with the eyes but with the mind" and that "the course of true love never did run smooth." Our personal grievances and tragic potentials are part of the wide tapestry of human experience.
The play within the play offers a metaphor for Shakespeare's audience, for the earnest desire Bottom eventually has to give the performance as a gift to the newlyweds involves an unselfish desire to serve the story. Similarly, Shakespeare's audience benefits by looking beneath the silliness of the fairyland story to see the darker impulses that are exorcised through this journey into a dreamlike fantasy theater offers.

We learn from A Midsummer Night's Dream that love is a form of madness. It may be many things, but rational it is not. Shakespeare, in this madcap frolic through love's landscape, offers many examples of the way love doesn't make sense.
Hermia, for example, refuses to marry Demetrius, even though he would be the rational choice. Demetrius was chosen for her by her father, and the law backs his right to pick his daughter's husband. As her father points out, there's nothing wrong Demetrius. Nevertheless, Hermia, in love with Lysander, instead flees to elope with her beloved.
Likewise, Titiania, a fairy queen, falls in love with the lowly Bottom, even though he has an ass's head. This is attributed to fairy magic, but what is the world of fairies and magic other than a world of fantasy and irrationality? (Even the play questions its reality.) Titiana, in her affection for Bottom, illustrates that love is blind and more than a little crazy.
Helena shows love's irrationality in her mad pursuit of Demetrius. This reveals the darker side of love's madness: she is willing to put up with abuse to be with her beloved.
Puck is only too accurate when he states, about humans and love: "Lord, what fools these mortals be." But humans would not want it any other way.

This play teaches us you can’t force someone to love someone else. This is a general issue in the play. Egeus tries to choose a spouse for his daughter against her wishes. In another situation, the potion Puck is given by Oberon causes trouble because it tricks people into thinking they are in love with someone when they really aren’t. The love is not real. You cannot force someone to be in love. If the love is not real, then chaos will result. That is what happens with the mismatched lovers in the forest.
In the end, the story has a happy ending because everyone ends up with the right person—the person he or she chooses. Theseus and Hippolyta choose each other from the beginning, and the play ends with their wedding and with all the other pairs successfully matched.