That link up above gives a pretty good account. She was signed previously by another label but they wouldn't let her do her own material.
Quote:...in early May 2005 she was hired as a staff songwriter – the youngest ever, still 14 – at the Sony/ATV publishing house...By age 15, she also walked away from an earlier 2003 deal she had made with RCA Records. The company wanted to extend her another one-year offer, but they refused to allow her to record her own songs. Taylor was not excited about their tepid one-year offer and she was set on doing her own material.
...Borchetta had heard a bit about Swift and knew she was a young songwriter over at Sony. He invited her to drop by his office to play some of her songs. He then watched her perform at Nashville’s Bluebird Café where she was being showcased one night. Taylor later recalled watching him in the audience that night as she performed, and noticed that he “was the only one who had his eyes closed and was totally into the music.” But Borchetta had competitors in the café that night, as he later told CBS. “There were several other record companies that were in the room. And I’m looking around, I’m going, ‘I hope none of these other guys are getting it.’” Borchetta liked what he heard that night, and soon called Taylor to a meeting. What Borchetta was planning was a new record label and he wanted Taylor Swift to be a part of that – an independent label that would take on the major Nashville Music Row companies. That sounded perfect to Taylor who seemed to like long odds and shaking things up.