‘Sooner’ is actually a derogatory term, and basically means someone who steals land.
Historically, it was the term for a group of American settlers who swept down to claim property that was part of the “Unassigned Lands.” This occurred before the “official” start of the land run, the Indian Appropriation Act of 1889, which was declared by President Benjamin Harrison.
Settlers who raced to claim the land opened by President Harrison’s decree said that the sooners “cheated” by grabbing the land and settling on it “too soon” – hence the term, sooners.
The 1992 movie Far and Away, which featured Tom Cruise and Nicole Kidman, depicted the drama of the sooners versus the legal settlers, from the illegal means by which sooners defended their land, and the ensuing court battles. One famous case is Smith v. Townsend in 1893.
Many people use the term sooner and boomer interchangeably, though the two are different. Boomers raided property, violently evicting the American Indians from it. They believed Indian lands were open for possession and settlement, but the government deemed this illegal and removed the boomers from the stolen land.
Eventually sooner lost that negative connotation and came to represent the passionate pioneering spirit. Since the sooner lands became part of the Oklahama territory, the University of Oklahama made it the name of its football team. Due to that, the term sooner became associated with the school. It is used in reference to the athletes that belong to its sports teams (plus their fans), as well as the school graduates and current student population.