The world of Athens and the world of the fairies mirror each other as monarchies. Both Theseus and Oberon are wise, if patriarchal, rulers. Each has a strong consort (or soon-to-be consort). Titania willingly stands up to Oberon over the Indian boy and Theseus has to conquer Hippolyta, queen of the Amazons, to earn her hand. Both rulers "win" against the women they love: Theseus wins Hippolyta as his bride and "jealous" Oberon wins the Indian boy and wins as well by regaining the attention of Titania.
Love matters in both worlds. In Athens, Lysander and Hermia are in love, Demetrius loves Hermia and Helena loves Demetrius. This spills over into the forest. In the forest, Titania falls in love with Bottom and Oberon's jealous love of Titania motivates him to want to take possession of the Indian boy she dotes on.
Nothing like the fairies exists in Athens, however, and Shakespeare does not afford us lush descriptions of Athens, as he does of the fairy realm, where the tiny creatures flit and fly. Athens is more representative of order and rationality than the forest--after all the lovers head for the forest to escape this restrictive order--and the forest more representative of the poetic, lunatic (after all, the action unfolds at night, under the moon) and imaginative.
One might argue, however, that the Mechanical are a comic parody of the fairies. If Puck bungles the love potions, disturbing the "script" of the love story that Oberon wants to enact, so the mechanicals bungle their lines. In both worlds, comedy, broadly construed (ie, nothing tragic happens) reigns.