Wait, what? Is this like a yearly state park pass? Or is this paid every time you want to go take a walk in the woods?
If you get a hiking permit, you are probably carrying a tent. The permits would allow the park management to limit and track the number of people out in the park wilderness areas at any given time, and prevent overuse or overly inconsiderate visitors. The permit application process may also discourage casual or inexperienced campers, who may have insufficient skill to explore backcountry trails without injury--including bear-related injuries.
You can see what a dayhike permit application looks like at the very bottom of this page: http://www.sgwa.org/permit.htm. Overnight (camping) permits are separate.