The simpliest way to say it is that groundspeed is true airspeed corrected for wind. Say you're flying along at 150kts into a 10kt headwind. You'll be moving through the air at 150kts, but only moving along the ground at 140kts.
Now for some of the various airspeeds:
Indicated airspeed (IAS): What the pilot reads off the airspeed indicator
Calibrated airspeed (CAS): Indicated airspeed corrected for instrument error
Equivalent airspeed (EAS): Calibrated airspeed corrected for the compressibility of air
True airspeed (TAS): Airspeed at which the aircraft is moving through the air. Will be different than EAS unless you are at sea level with a standard aptmosphere due to changes in air density affecting instrument readouts.
Most of the time, at least in general aviation, all we care about is indicated airspeed (for performance related issues such as climb speed and such), true airspeed (which can be calculated knowing pressure altitude and temperature) to know how fast we're actually moving through the air, and groundspeed (which can be found from various instruments such as a GPS or DME
) to know how fast we're actually making our way to our destination.