Disappear or untraceable. 

Different people use this term in different ways.  I believe it began as a reference to the "power grid", meaning that you're not using any electricity.  I've also heard some people use it simply to mean no longer using a cell phone.

But, in my opinion, to truly "go off the grid", you would have to do both of the above, along with other things like only using cash (no credit cards), no loans, no car, no public utilities; basically, nothing that could allow any business or government to track your actions.

"go off the grid" means the person disappeared in the sense that the person was fairly regular in your realm (or world) and abruptly (or suddenly) was gone where it seemed impossible to contact them.

This topic would be more appropriately placed in the " Ask a question "

Anyway, Off the grid means not connected in a network.
When applied to electrical power, as the most common use of the phrase, it means to generate your own electricity with solar or wind power.

It could also mean giving up a cellular phone.

Living off the grid, means being in a remote location.

Any person off-the-grid is untraceable and cannot be reached.

Today's society has facebook and twitter and even here in italki website and we are connected.
Give it all up, and you are off-the-grid.:)