As others have noted, Gatsby, then James Gatz, felt humiliated at having to work his way through St. Olaf's college as a janitor. This reveals much about him: he was ambitious, he was proud, and he believed he was destined for a better life than the dull path offered him: "the drums of his destiny" beat in his ears, if nobody else's. It also shows personal characteristics that are perhaps as much flaws as attributes: Gatsby is impatient, unwilling to wait around for success to happen the ordinary way, and willing to break the rules to get ahead. He tellingly only lasts two weeks at St. Olaf's, a very short time. He clearly doesn't like to compromise, and he isn't about to let other people dictate what his "script" for success should be. In his leaving St. Olaf's, a Lutheran college, we see a definitive break with the more puritanical, younger self, the self who wrote the notes on self-improvement that his father will proudly show to Nick at Gatsby's funeral. Gatsby will continue to struggle to improve, but it will be on his own terms. We also can see in this the seeds of what will attract Gatsby to Daisy: she has around her the aura of money, prosperity, and security that James Gatz lacked.
Gatsby's dropping out of college was an important moment in this life. We find out that he attended a small college in Minnesota, St. Olaf's college (it's a real college, if you are wondering). Because Gatsby grew up poor, he had to work his way through college. He was a janitor to pay his tuition.
After two weeks he could not bear working because of the humiliation. So, he left and worked for a man whom he met as a fisherman on Lake Superior. This man, Dan Cody, took him under his wing. Cody was a self-made millionaire.
Cody made Gatsby his personal assistant. On their subsequent voyages to the West Indies and the Barbary Coast, Gatsby became passionate about wealth and getting ahead.
From this perspective, Gatsby's leaving college made all the difference in his life. From that point, his hunger for wealth, which was borne out of a desire to win Daisy, consumed his life.
Gatsby was frustrated at trying to pay his way through college by working as a janitor. "He stayed there two weeks, dismayed at its ferocious indifference to the drums of his destiny, to destiny itself, and despising the janitor's work with which he was to pay his way through."
So, he dropped out, started wandering the banks of Lake Superior, and eventually bumped into Dan Cody...thus follows the transformation of James Gatz into Jay Gatsby.