"Off the grid" pertains to a lifestyle characterized by the lack of a paper trail (for example, no Social Security number, driver's license), or a fake identity. People living off the grid may take jobs that pay under the table, move from place to place, and take on numerous identities.
In the Terminator franchise, living off the grid is a way to avoid attack by Terminators sent from the future by Skynet.
T2: Infiltrator
Sarah Connor lives off the grid since the Cyberdyne Systems headquarters incident.
Terminator 3: Rise of the Machines
John Connor was living off the grid in order to avoid detection by agents of Skynet. The fact that he inadvertently ran into Kate Brewster was the only reason that the T-X and T-850 found him.
Terminator: The Sarah Connor Chronicles
Sarah Connor and John Connor live off the grid since the Cyberdyne Systems headquarters incident.