A GFCI device measures the current going out on the hot conductor against the current coming back on the neutral. When those two numbers stop matching, current is going somewhere it shouldn't — often through a person — and the device opens the circuit in milliseconds. It is one of the cheapest pieces of life safety equipment in a building.
The list of places the code requires it has grown steadily since the 1970s, when it applied only to outdoor receptacles and pool equipment. It now covers bathrooms, kitchen countertop receptacles, garages, unfinished basements and crawl spaces, laundry areas, outdoors, and receptacles within six feet of any sink. Recent code cycles have extended it further, including to certain 240-volt appliance circuits.
This is why homes built to code in their own era can be legitimately unprotected today. A 1978 house in Farmers Branch that has never been remodeled may have exactly one GFCI in the whole building — outside, by the hose bib — because that is all that was required when it was wired. Nothing was done wrong; the requirement simply moved.
The fix is usually inexpensive. In many cases a single GFCI receptacle installed at the first device on a circuit will protect everything downstream of it, which is a much cheaper path than replacing every outlet in the room. Where the circuit layout doesn't allow that, a GFCI breaker at the panel does the same job.
One practical note: GFCI devices have a finite life and a test button for a reason. Press it monthly. If the device doesn't trip when you press test, or won't reset afterward, it has failed and needs replacing — a dead GFCI provides exactly as much protection as no GFCI at all.