In its simplest form "the grid" is the power grid that connects homes all over the country which provides them with mains power.
When you are connected to the mains power grid you are referred to as grid-tied or vice versa tied to the grid. So Off-Grid simply means operating your own power not tied to the nationwide grid.
When you go bush or remove yourself from your device people quite often refer to this as going-off-the-grid. Not quite the same but it might be where some people associate off-grid with being remote or removed. It doesn't mean without technology though as a modern-day off-grid setup can actually be smarter and more intuitive than your current smart meter.
In-fact building your own power source with battery backup, solar and grid independence gives your location the ability to store, sell, distribute, manage, monitor, and action your power in almost unlimited ways. All with the benefit of resilience to outside infrastructure, outages, or scheduled power cuts. The components and hardware used in grid and off grid should be from a quality internationally recognised brand as the hardware should be assessed as a system costs that you can calculate over a 20 year period for a good return on your investment.
There is another variation from grid or off-grid. It's really a hybrid of the two systems taking the best of both and in recent years its becoming more and more common. Grid-tied with battery backup has been around for some 15+ years but marketing by Telsa and the Teslawall has made everyone aware of its existence. LG chem and others have similar "wall" designs which give people options for internal or external system storage designs.