Willie Hawkins was a professional baseball player for the New York Giants in 1953. As the lone Negro on the team, he was admired by the people of the largely black Harlem neighborhood, but to most whites of the time, he was, as he remarked, "just another colored man that can hit a curve ball."
Willie Hawkins was part of Benjamin Sisko's visions from the Prophets and the Pah-wraiths. He had pursued Cassie, Benny Russell's fiancé, at some point and often hit on her, only half-jokingly. (DS9: "Far Beyond the Stars")
Willie Hawkins was portrayed by Michael Dorn, whose usual Star Trek role was Worf. In fact, the role of Hawkins was Dorn's only appearance without prosthetic makeup. He noted, "I just loved not being in makeup." (Cinefantastique, Vol. 32, Nos. 4/5, p. 93) After enthusing that he found the experience "wonderful," Dorn went on to say, "But the 'wonderfullness' of the filming always had the caveat that it would be over soon and I'd be back in Worf-dom. So I enjoyed it to the fullest when it was happening....". 
Although there was no real Willie Hawkins, the character is probably based on the similarly named Willie Mays, who played for the Giants from 1951-1971 but ironically not in 1953, as he was serving in the military during the latter stages of the Korean War. In one of Sisko's early visions in the episode, when he sees Hawkins on Deep Space 9, his uniform number, 42, is the inversion of Mays' number; it was also the number of Jackie Robinson, the first "Negro" player in Major League Baseball. Also, in a game against the Brooklyn Dodgers, he supposedly "robbed Snider of a tater [home run]." This is a reference to Duke Snider, an outfielder with the Dodgers who played at the same time as Mays and was a major rival. Prior to this episode, in the Season 5 episode "In the Cards" (which was directed by Dorn), Jake Sisko and Nog had made a series of increasingly complicated trades to acquire a Willie Mays trading card for Jake's father, a diehard baseball fan.
Willie's surname comes from the script.
In an early version of the script, this character was a boxer, not a baseball player. He was romantically involved with a white woman, which was discovered by Kevin Mulkahey and Burt Ryan, who subsequently beat him to death. 
The authors of the Star Trek Encyclopedia (4th ed., vol. 1, p. 330) thought Willie Hawkins "might have existed in some alternate reality, or perhaps only in certain reaches of Ben Sisko's mind."