No, it's a free permit to hike in a park for a day. They want to track trail usage, and sometimes implement quotas to prevent overuse. There are occasionally rangers who patrol the trails and check for permits, but it's pretty rare. You may also need a separate parking permit for national forests (adventure pass), but apparently it's been ruled unconstitutional by the CA supreme court. Many trails in national forests/state parks in California require day hike permits (generally the good forested ones do).

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.

If you get a yearly state park pass, you're probably walking on the trails no more than 10 km from the parking lot at their furthest points, and leaving before the park closes for the night.

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.