Targs were foraging animals native to Qo'noS which somewhat resembled Terran boars with spikes on their backs. The Klingons enjoyed hunting wild targ but also maintained agricultural herds for consumption and commonly kept targs as pets.
Despite the popularity of targ hunting, targs were so abundant on Qo'noS that herds could be a collision hazard; Klingon ground assault vehicles used targ scoops to clear the animals away from their path. (VOY episode: "Elogium")
Targs were also quite common on worlds throughout the Klingon Empire and it was not unusual to find live targs on Klingon starships where they were kept for food. (Star Trek video game: Away Team; ENT episode: "Sleeping Dogs"; TOS movie: Star Trek III: The Search for Spock)
Martok was glad to have his friend Worf made an Ambassador - as it would mean he had an ambassador to go targ hunting with. Worf himself owned one as a child; years before living on Gault. (DS9 episode & novelization: What You Leave Behind; DS9 - Tales of the Dominion War short story: "Requital"; TNG episode: "Where No One Has Gone Before"; TNG novel: The Eyes of the Beholders)