The net is a tool that's used to catch small animals, most notably insects. When you catch an animal with the net, you will always be given insect parts unless you successfully catch a butterfly, in which case you will be given it in the form of an item. It's a reliable tool to have in one's possession as it greatly helps with fishing to be able to have much bait, and the butterflies gotten from it are very useful for carring many objects.
Hitting with net in hand causes no damage, thus one can hit animals for fun, or obtain infinite resources by hitting trees, rocks, bushes or cotton plants. And it can be useful for herd Sheep