Frank Ross is Mattie's father, but he seems to exist in the novel as a plot device more than a character. We really only get a good look at him through reminiscences and memories—like the sheriff, who tells Mattie that her father "impressed me greatly with his manly qualities. He was a close trader but he acted the gentleman" (3.14), or Mattie's insistence that her father interfered because "Chaney was a tenant and Papa felt responsibility. He was his brother's keeper" (1.15).
These two quotations aren't much, but we can still build a good picture of Frank. He was adventurous, bold, a good businessman, and a devoted family man … with an intense code of honor, one which might have just got him killed. As Chaney's employer Frank felt the need to try to stop him from getting in trouble when he was drunk—even when Chaney's response involved a fatal bullet. And that makes him an interesting contrast to Rooster and LaBoeuf, the other men in Mattie's life: they live up to their codes of honor by killing; Frank lives up to his by being killed.
And in the end, maybe Frank is why Mattie never marries: no man can live up to him.