By the time Aegeus was ruling Athens, just before the launch of the Trojan War, the Navy of Crete was very strong and the Minoans, who were living in Crete, were attacking and terrorizing Greek cities.
In order to leave the city of Athens in peace, the Athenians made a pact with the King of the Minoans, Minos. Every nine years they had to send a tribute of seven Athenian boys and seven Athenian girls to Crete, where they were devoured by the Minotaur, the dreadful monster of Minos that was half-human and half-bull. Only if somebody killed the Minotaur would this torture come to an end.
Every time the Athenians had to send children to Crete, the whole city was in grief and despair. Theseus, the hero of Athens, could not bear this situation and, much to the dismay of his father, he decided to help the Athenians and kill the Minotaur.
So one day, he took the place of a youth that should be sent and got into the boat for Crete. The boat was having a black sail, as an expression of the Athenians' mourning. Theseus promised his father that, in case he achieved victory, he would hoist white sails- if he failed, this would mean failure and the sails would remain black.
When Theseus and the other children arrived in Crete, King Minos and his daughter Ariadne were already expecting the party. Immediately, King Minos ordered to send them in to the Minotaur to be devoured the next day. But Ariadne fell in love with Theseus and wouldn't allow any harm to him. So, the other day, when the youth was sent to the Minotaur, Ariadne gave Theseus a sword and a ball of thread to find his way out of Minotaur's Labyrinth. [See: Theseus and Ariadne's thread]. This way, Theseus and the other children managed to escape from the monster and rushed into the vessel to escape. Ariadne followed them.
On their way back home, the children were so full of joy that they forgot to change the black sail. King Aegeus was expecting them, standing on a high rock and staring at the sea. When he saw the vessel coming and realized the sails were black, he fell fainting into the sea and died. In memory and honor of King Aegeus, the sea has been named the "Aegean Sea".