You should be able to descend on loose trails without sliding your rear wheel or be willing to walk your bike down these sections. You should be able to ride over water bars or be willing to walk your bike over them. You should be able to ride around sharp corners without sliding or be willing to walk your bike around them. You should be willing to avoid cutting switchbacks. You should be willing to get off your bike and walk it through wet or muddy sections and to wait for a trail to dry out after a storm or after the snow melts.
Many public lands require that helmets be worn.
Many public lands are open only between sunrise and sunset. Not all singletracks within public lands are open to mountain biking. It is your responsibility to make sure that you are riding on legal trails. Be sure to check the local regulations when you arrive at the trailhead. A rolling tire on a hard surface does not cause significant impact.