He is Tohru's late father and used to be a student teacher when he met Kyoko Honda (who he helped leave her previous lifestyle). He later left student teaching and married Kyoko, despite the eight-year age gap (when he and Kyoko met, she was 13 and he was 21). Katsuya, who had apparently had a rebellious childhood, admitted that he had fallen in love with Kyoko because she had been able to cry and confess to being lonely, which he wasn't able to do. When Kyoko told him she was pregnant and had doubts as to whether she could properly raise a child, he assures her that they will take care of the baby together, as a real family.

Spoiler

A short time later, when Tohru was three years old, he died of pneumonia. The sudden death caused Kyoko to almost kill herself.

(Source: Wikipedia)