Nick and Tom know each other from their days together in university. Both men attended Yale, which Nick explains when he first introduces Tom, whom he characterizes as "one of the most powerful ends that ever played football at New Haven [...] one of those men who reach such an acute limited excellence at twenty-one that everything afterward savors of anticlimax" (Fitzgerald 6). Tom is also incredibly wealthy, which is in part the reason for Nick's other connection to him: Daisy, Nick's cousin, is married to Tom.
The way in which Nick introduces Tom's character sets him up for further development along these same lines: powerful, wealthy, and violent. Over the course of the novel, Tom's actions and statements reinforce him as a character to which not only Gatsby but Nick himself is compared.
Nick knows Tom Buchanan from their undergraduate days at Yale where Tom had been a standout football player. They were in the same senior society, and Nick explains that though they were not close, he sensed that Tom "approved of" him and wanted him to "like him with some harsh, defiant wistfulness of his own." After Yale, Tom returned to his hometown of Chicago, and supported by his family's "enormous" wealth, married Nick's second cousin once removed, Daisy Fay, of Louisville. Nick recalls staying with them for two days after he returned from his WWI service in Europe. After a brief period in France "for no particular reason", Daisy and Tom moved to East Egg, one of the novel's fictionalized Long Island settings. It is there, in the spring of 1922, that Nick becomes reacquainted with both Tom and Daisy. In the novel's opening chapter Nick visits them at their home, and his description of Tom's physique ("a cruel body"), attitude ("a supercilious manner") and boastfulness ("I've got a nice place here") signals to the reader that he has, in fact, failed to earn Nick's liking. By the end of the evening Nick has learned that Tom is an unfaithful husband and has also been physically rough with Daisy.
Fitzgerald, F. Scott. The Great Gatsby. Charles Scribner's Sons, 1925.