Rubber and Leather Tramps are descriptions that vagabonds use to describe a person's method of transportation. A rubber tramp has a car or other wheeled vehicle, and travels on the rubber tires. A leather tramp has no vehicle, and travels on foot, shoes often being made of leather. The distinction comes from both ease of travel -- a rubber tramp is more able to decide destination than one who relies on hitchhiking -- and an unofficial status: rubber tramps are sometimes seen as "less valid" than leather tramps because their vehicle is viewed as a luxury item. Chris started out as a rubber tramp in his old Datsun car, but soon found the opportunity to change his status:

With the battery dead there was no way to get the Datsun running. [...] Instead of feeling distraught over this turn of events, moreover, McCandless was exhilarated: He saw the flash flood as an opportunity to shed unnecessary baggage.
(Krakauer, Into the Wild, amazon.com)

As Chris had specific ideals about his vagabonding, he turned the abandonment of his car into a life event; he buried some of his possessions to recollect later and burned his money, throwing off the shackles of monetary and material goods to travel alone. In a way, the transformation of Chris from rubber to leather tramp acted as a turning point for him, allowing him to more fully realize his dreams of wandering the country without ties to society.