That’s right, most of the island is a National Park.
Virgin Islands National Park encompasses over half the island of St. John preserving stories of the prehistoric past and over a hundred historic sites that together complete one the most undisturbed and comprehensive Caribbean landscapes.
There is no charge for entrance into Virgin Islands National Park.
However, a same-day user fee of $4 is collected at TrunkBay.
Here is the official link:
Virgin Islands National Park
You can check the website for lots of useful information including history, events and hiking trails.
There is also a nice map here.