These setting represent the three world of the play.
Athens is the world of the court. It is a world of power and laws. It is evident that it is a world ruled by men. Thesus won Hippolyta by defeating her in battle. She is the Queen of the Amazons and a powerful female force who has entered this masculine world. Perhaps it is her presence which gives Hermia the courage to defy her father. It is also more of a daylight world. One could even say, the "real" world.
The second world is the world of the workers. Peter Quince and his crew of "rude mechanical" represents the everyday world of everyday people, not the aristocracy who live in a different world, but the world of the the average worker/craftsman in Athens. By desiring to perform a play to celebrate the wedding, they intersect with both the world of the court and the world of the woods.
The third world is nighttime woods aka fairyland. It is in this world that magic rules dreams. Oberon, Puck, and Titiana all have magical powers and they use these powers in various ways.
The three worlds of the play are all important in the telling of the story.
I have seen productions of this play in which the parts of Thesus/Oberon and Hippolyta/Titiana are doubled by the actors. This gives us the duality of human nature and perhaps that is how it was orignially performed due to the size of the company.
This question has already been asked and answered many times here on eNotes. Here is a comprehensive link for you: http://www.enotes.com/midsummer-nights-dream/q-and-a/tags/setting
Woods represent irrational behaviour, dreams, magic, confusion and immature love. This is the "fairy world"
Athens represents rationality, mature love (theseus and hypolyta), obstacle for lovers, the realistic world (no magical, real!).
This is the world of the "Young lovers"
The mechanicals' world might represent simplicity and true happiness, because if you think about it, the person who is/ will be truly happy in the end is noone, but Bottom. He gets Titania's true love, and doesn't even care about losing it because he thinks of it as a dream.
Hermia's love towards Lysander was based on looks and perhaps, drama. Now that the drama is over, the love may not last.
In Helena's case, what if the love potion wears off??!!