Rope is super useful for many things, at many technology levels, relating to procuring and preserving food:
- Snare Traps rely on ropes for the snares
- Fishing, either with nets or with a rod, will require string or rope to make the correct tools
- Buildings, for food storage, may rely on ropes for lashing.
- Smoking requires an enclosed space for the smoke to preserve food. Once again, rope comes to the rescue and provides material for lashing.
- Rope can be used to make cord baskets, allowing people to gather more per trip.
- Fencing and deer scares to fend off herbivores. Deer get a little freaked out when they get touched by something they don't see, and a thin rope could be that thing!
And I am sure there are more! Like making rope ladders to get high-up fruit, making a bow, starting fires (bow drill), measuring farmland/plots, trellises for climbing vines, and others...
I suggest looking at youtube channel "Primitive Technology" to see how much rope is used in various projects, including food projects, in a very low tech setting. As a bonus, this all takes place in an Australian forest!
FROM THE COMMENTS:
The comments have had yet more suggested uses or expand upon suggested uses. Lashings for boats/rafts (@Alexander the 1st) and harness for beasts of burden (@workerjoe) are two big ones.
In any case, I tried to keep my list as general as possible, making as few assumptions as possible about what kind of forest, what the climate is, what people eat, etc.
Obviously, the technology and climate of the forest village in question affects how they use rope, but the consensus is clearly that rope/cordage is very useful and important to pre-industrial-revolution hunting, gathering, trapping, and farming. (Even then, I bet a modern farmer can expound the virtues and usefulness of cordage!)