Katniss's Mom is a skilled healer, though she suffered from severe depression after Katniss's father died. For this, Katniss greatly resents her. Katniss's mother is not the survivor that her daughter is. We also learn that Katniss's mother gave up a life with her well-off parents to marry Katniss's father, a poor coal miner. Peeta's father was also in love with Katniss's mother.
Katniss's father, on the other hand, is almost entirely absent from the book. He was a coal miner in the Seam of District 12 who died in a terrible explosion when Katniss was 11. He was a strong provider for his family. After his death, Katniss stepped into his place and filled his shoes by becoming the sole provider for the family.
We also learn that Katniss's father had quite a spirit: he loved music, for example, and taught his daughter to use a bow and arrow. Though he is gone now, it is clear that he played a very large part in shaping his daughter's personality.