Back in the day, the gods did not like it when humans tried to act like them by overcoming their mortal limits. In ancient Greek culture, acting like a god was called "hubris", and it was often severely punished. Flying through the air definitely constituted hubris, since flight was supposed to be a strictly gods-only activity. Watching from the ground, shepherds and plowmen even mistake Daedalus and Icarus for gods, since mortals had never before achieved flight.
Of course, Daedalus and Icarus pay a price for overstepping their humanly bounds. Icarus dies and Daedalus loses a child—lose-lose. It's an important lesson in humility, and the wisdom of living within your limits. The myth seems to be saying that instead of wanting something extraordinary (such as flying, or in Icarus' case, flying really high), we should learn to be happy with what we already have.
Daedalus takes this lesson in humility to heart. It's not an accident that when he lands in Sicily, he builds a temple to Apollo, the god of the sun. After watching his son be destroyed by the sun, Daedalus has accepted that he's just not as powerful as the gods or nature. By building the temple, he's essentially saying, "Sorry, Apollo. I totally respect you now. And just to prove it, I built you this totally swanky house of worship, complete with a bunch of beautiful statues."
In a bit of poetic justice, the writer Ovid says that Daedalus' nephew—whom Daedalus had tried to kill by pushing him off the Acropolis—watches as the inventor performs the funeral rites for his son. (Daedalus doesn't notice the nephew, since Athena had transformed him into a partridge.) Apparently, Daedalus didn't think twice about pushing his nephew off a cliff, but when his own son fell from a great height? Well, that's a different story.