1) Living without using the services of public or private utility companies (grids) such as electric, gas, or water, by generating and providing for one's needs such as by using solar power, etc.
2) One who disdains all recordable common forms of commerce, such as eschewing any form of credit extension, banking services or reportable payroll activities, using only cash so as to avoid any traceable transactions, e.g., living completely 'underground.'
Famous "off the grid" people include such disparate types as environmental champion Daryl Hannah and sociopathic Luddite Ted Kaczynski.
1) Bob lived off the grid in his rustic cabin in the mountains, where he provided for all his own means.
2) Leaving behind no record of his existance other than his birth certificate and social security number, Jim lived totally off the grid.