The network of electrical power lines from which power companies buy electricity. Modern usage of this term suggests a desire to be independent from grid-transmitted electricity (including water lines, sewer mains, and supermarkets). Meaning many people, disillusioned with western civilization's dependence upon all things consumable, are reverting back to windmills, solar power, and other forms of homegrown energy, to promote self-reliance in an effort to get "off the grid."
Its meaning has extended to a few other uses, including not wanting to be "in the system" (for example, not wanting to give out your social security number to anyone and everyone). In another sense, "going off the grid" is an expression for creativity, similar to "thinking outside the box."