How are the woods beyond the fence important to katniss?

Answer 1

That's where Katniss goes to hunt, so they're important in a practical sense. But more than that, it's where she feels capable, even free.

Answer 2

It was the place where she and Gale could be themselves and they didn't have to hide anything. It was their one place of sanctuary

Answer 3

They are important because they helped her get food