The "grid" refers to the electricity grid, so dropping off the grid literally means disconnecting from the power grid. People who do this tend to be moving away from urban life into the wilderness. By extension, the phrase means cutting oneself off from society, going somewhere else to start a new life, disappearing or even hiding (from the police, for example).

Drop off the grid means to disappear forever or for a short amount of time. Example: My friend dropped off the grid when she was traveling through Europe.

It means to lay low or dissappear, as an example: the soldier "dropped off the grid waiting for back up", it means he was hiding until the reinforcement show up to the rescue

Dissappear without a trace