From hours of extensive research, I have gathered that Kelly Clarkson sings professionally. That makes her a logical choice to sing the national anthem at the Super Bowl. The Star Spangled Banner was once performed at the Super Bowl by marching bands and other instrumentalists, but it's recently become a way for pop stars to promote themselves. I have no idea whether or not record labels pay the NFL to get their artist to sing the national anthem at the Super Bowl, but this seems like a safe assumption.
This is not to diminish the accomplishments or vocal acumen of Ms. Clarkson, it just seems terribly unlikely that there was some kind of extensive merit-based selection criteria. But hey, she knows how to sing, so it will probably be good!
For those interested, the last instrumental national anthem performed at the Super Bowl was performed by trumpeter Herb Alpert at Super Bowl XXII in San Diego.