Hunting is an action that can only be performed in the forest. Sims that are capable of combat (the Spy, Knight, and Monarch) are the only sims who are able to hunt. Technically, whaling can be considered a form of hunting (which can be performed by any sims with the "Whale Ate My Parents" trait), but only results in whale meat, whereas hunting can result in several.
These meats can be hunted for in the Forest or bought from the Village Shoppe. Whale meat is from successful whale hunts on the High Seas. Random Events can also reward meat.