What is a brood sow, and how does its loss affect the Baxter Family?

A brood-sow is a female pig kept for the purposes of breeding. In The Yearling, the Baxter family own a black brood-sow by the name of Betsy. One morning, Penny and Jody are shocked to discover Betsy's mangled corpse. The poor pig has been attacked and killed by Slewfoot, a big old bear who lives in the forest. As a brood-sow, Betsy would not have been slaughtered for meat, so she became almost like a family pet. As one can imagine, Penny and his son are pretty upset at the death of one of their most beloved animals. But they're also determined to track down the vicious swine-killing bear to his lair and finish him off.
Unfortunately, the big showdown between man and bear turns out to be a bit of a fiasco. Penny's gun backfires, and one of this hunting dogs—Old Julia—ends up being injured by the ferocious bear. Much to Jody's disgust, it's only after the bear has successfully escaped into the forest that their "feist," or small hunting dog, returns to the party. So much for the dog's hunting skills.