Here's a very simple graphic of what you could be seeing:
(source: cadblog.net)
And this is why we land into a headwind rather than the tailwind, since otherwise we would land at a faster speed and require more runway to stop.
GPS measures ground speed, or absolute speed. The pitot tube on the aircraft will measure the speed relative to the airflow around the aircraft.
Here's som helpful graphic from NASA on relative velocity:
Footnote: As Ratchet Freak demonstrates in his equation, you have to of course remember that this is simplifying it as flying straight into the wind and not taking account of the wind direction.
