The most important time to hug a tree is when your lost. It provides comfort, shelter and keeps you in one place.
Besides the literal hugging of a tree, there is the metaphorical. it is important to treat the trees and environment with respect. If you do any wheeling it is outside. You cherish the thrill and excitement of crawling over hills, rocks and sometimes logs. To keep these privileges you need to follow the outdoor code and be considerate of the outdoors and conservation minded. Leave it cleaner than you found it, leaving nothing but footprints.
If your not the outdoors type, consider what trees do for us: they provide oxygen, warmth and shelter.
Of course you could just try hugging a tree and see what you get out of it. Curiosity kills the cat.