Anything that's off-grid doesn't use public utilities like electricity or water. Your dream house might be an off-grid cabin, but you should probably try using an outhouse in the winter before you actually move into one!
Off-grid sometimes refers specifically to the national grid, which is made up of regional power plants that provide electricity to most Americans. If solar panels on your roof generate all your electricity, you live in an off-grid home. It can also mean "outside of and not dependent on society" more generally: "I wanted an off-grid life, so I moved into the woods and got some chickens and goats."