Unowned / Federal land was offered to settlers through the Homestead Act of 1862. The act provided that a settler could claim 160 acres of public land, and those who lived on the land for five years, and who improved the land during that time would actually be given ownership of the land.
One of the Indian Appropriations Acts (the one in 1889), tried to make the land claiming equal by saying that anyone who claimed land before a certain time would not be able to homestead on that land. This became known as the "sooner clause," so basically "sooners" were seen as cheaters and thieves.
Later, the negative connotation of the word changed, and perhaps because it was an old pioneerish type word, people started thinking that sooners were cool in a historical, "my roots go back this far" type of way. In 1908 the University of Oklahoma named their football team the "Sooners" and Oklahoma is now known as "The Sooner State."
The US state of Oklahoma is unofficially known as the Sooner State. Areas of land were to be opened for settlers to lay claim to, however it was illegal for any potential settler to enter the area before it was open. Those who entered the area early were called "Sooners."