In the novel, Nick says that Jay Gatsby had a "Platonic conception of himself." Plato was a philosopher that conerned himself with trying to define what was real and what was ideal. Gatsby decided he did not like the "real" Jay Gatsby, so he decided to create an ideal person and then live as if he really were that person. He finds a mentor for himself who is rich but when that man dies, he enlists in the Army, gets out, gets an Ivy League education, and then proceeds to accumulate wealth, even though in a shady way. He becomes what is called "nouveau riche" - newly rich. That is why he lives in West Egg and not East Egg, where the moneyed families live, the people that are born into money.
Gatsby thus creates an ideal of who he is and that is who he becomes in his own mind. The other characters do not buy into his Platonic idea of himself, sadly, and this leds to his destruction. He is always looking at the green light, but cannot attain it.
In Greek mythology, it is believed that the Godess Athena "sprang full grown from the head of Zeuss" so the use of the word "sprang" is also a reference to the Greeks, only mythology in this sense. The Jay Gatsby that appeared on the stage of East and West Egg "sprang" from his own creation, but Nick soon learns who the real Gatsby is when he meets Gatsby's father