This quotation is found in the Chorus of Christopher Marlowe's Doctor Faustus.
The Chorus introduces us to Doctor Faustus's character, starting with his infancy, and throughout his lifespan until the moment when he becomes a doctor and is described as someone who is capable of
Excelling all whose sweet delight disputes.
What this entails is that our main character is a prodigious man, indeed, gifted with qualities that allow him to be even better than his own peers.
However, the Chorus detours from this and explains that Doctor Faustus, rather than becoming humbled by the fact that he has so much talent bestowed upon, he instead gets too much of a high opinion of himself.
Till swollen with cunning, of a self-conceit =(his expertise in matters makes his ego swell)
The part that reads,
His waxen wings did mount above his reach
is allegorical to the myth of Icarus, the mythological son of Dedalus.
In the myth of Icarus, Dedalus is a master builder and craftsman who is known in mythology for building the labyrinth that withheld the minotaur. After being punished along with his son Icarus for a separate indiscretion involving Minos and Pasiphae, Dedalus created an escape route by air to leave Crete with his son. He created wings, made out of feathers held together by wax. Wax is a sensitive substance, for which Dedalus toldIcarus not to fly too close to the sun, or to close to the sea. However, Icarus got so excited with flying that he lost himself and flew too close to the sun. Hence, his wings melted and he fell into the ocean.
Similarly, Doctor Faustus becomes so big for his own good that he "flies too close the sun". This is a way of saying that he thought so highly of himself that, like Icarus, he gets too close to a dangerous point.
And, melting, Heavens conspired his overthrow;
Therefore, since Faustus is so obsessed with being better than everyone else, fate will teach him a lesson by "melting his wings" (drop him down to reality), and by punishing him (heavens conspired his overthrow).