"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.
Terminator 3: Rise of the Machines
John Connor was living off the grid fearing the possible future. Subsequently Skynet had no registers of him in 2004, and only the fact that John inadvertently ran into Kate Brewster made the T-X and T-850 find him.
Terminator: The Sarah Connor Chronicles
After losing her parents to the T-1000 and being adopted by the Guardian T-800, Sarah Connor presumably lived off the grid along with the Terminator from 1973 to 1984. (Kyle even mentions that "You haven't had a proper relationship with a human being since you were a kid.") Consequently, once Sarah time travels to 2017 and is arrested, the San Francisco Police Department can't find any information on her in neither the government database nor social network.