It's a basic thought that Leave No Trace principles require that you stay on the established trail. But that's simply not always the case, and you should learn how to leave the least amount of impact possible if you do go off trail.
Why People Say to "Stay on the Trail"
The basic reason behind saying "stay on established trails" is because vegetation and organisms on the tails themselves are already damaged beyond recovery, so you aren't worsening any problems by walking on them.
If you were to make a new trail, and everyone walks on the same spots as you, you'd then end up with this erosion happening in more areas as well. Concentrating travel on trails reduces the likelihood that multiple routes will develop and scar the landscape.
How to go "Off Trail"
Any movement that isn't on a designed trail (such as going to remote areas, searching for a bathroom area, or exploring near your campsite) is defined as off-trail.
There are two main that's that determine how off-trail travel will affect the land: durability of surfaces and vegetation, and frequency of travel (or group size).
Durability refers to the ability of surfaces or vegetation to withstand wear or remain in a stable condition. Rock, sand, gravel, ice, thick snow, and dry grasses are the best to walk on because they are resistant to being trampled leading others to follow in their footsteps. If you do have to walk on more sensitive vegetation, you want to walk a route that will not be directly followed by others: it's best if you all don't walk in the same spot over and over again.
Frequency of use and large group size increase the like hood that a large area will be trampled, or that a small area will be trampled multiple times.
In pristine sites it is best to spread out tents, avoid repetitive traffic routes, and move camp every night. The objective is to minimize the number of times any part of the site is trampled. In setting up camp, disperse tents and the kitchen on durable sites.