Ground speed is the actual speed over the ground. There are a number of ways of determining the ground speed of an aircraft that have been around since way before GPS existed.
If you know the winds aloft, you can determine your ground speed from your true airspeed, and you can determine your true airspeed from indicated airspeed (sometimes TAS is indicated directly in the cockpit). During the course of a flight you can infer ground speed from navigation fixes taken periodically. At one time, airline pilots determined their positions over the oceans by celestial navigation, which is why some older airliners still have "eyebrow" windows over the main windows in the cockpit.
If you have nearby VOR/DME stations, you can determine ground speed from those, too, irrespective of winds aloft. You can do it without DME, too, as long as you can determine your position over time.
Other navigation aids, such as inertial navigation systems and flight management systems on airliners, also provide ground speed, and they can do so even without GPS.
Essentially everything you can do with GPS could also be done before GPS, it just required a little more training and effort. It's all just a question of standard air navigation.