What was the hatchet good for and how did having it help Brian to survive his ordeal?

One of the first ways that the hatchet is important to Brian is that he feels it is something useful. When he takes inventory of the things he has, it is the one thing that he considers to be a useful tool.

The hatchet is what allows him to make fire. It takes him quite a while to figure out how to do it, but with the hatchet he can strike rock in order to make sparks and eventually get a fire going. This provides a great deal of comfort and the potential for cooking meat if he can get his hands on it.

He then uses it to make the fish spear and nearly all of the other tools and bits of shelter, etc. Perhaps he could have found a way to survive without it but as the story is told, it is likely the most important possession he had after the crash.