"Off the Grid" is a term used to describe people who to some degree have vanished from society's databanks. The term most likely comes from buildings that perform their own power generation and thus leave the power grid. The term has expanded in scope a little, and now encompasses those who live without credit, taxes, employment, or possibly even a permanent home.
My father-in-law, who uses solar electricity, passive solar and wood heating, and waste vegetable oil for his cars, told this story of someone he met in Florida, which is a common destination for road people.
A guy who does odd jobs for cash rents out an apartment in the back of a warehouse. He doesn't pay taxes because all his income is under-the-counter. He doesn't have a car. He doesn't pay any bills because that is included with his rent. He's basically off the grid by proxy, as the owner of the warehouse and the people who pay him are on the grid and must be so in order to have money with which to pay him or services to provide to him.
This man could certainly go further. Were he to lose his rented pseudo-apartment, he could still likely stay primarily in campgrounds. Transportation needs can be met by bicycle. If he could find permanent shelter, he could farm or gather food in the worst case. However, this scenario goes beyond going "off the grid"; "mountain man" is more apt, although Florida is pretty flat.
Off the Grid is also the name of an album and long-form music video by Octave One with Random Noise Generation and Kaotic Spatial Rhythms.