The way I like to explain it is imagine a person walking up an escalator. Your total speed is your walking speed (air speed) plus the escalator speed combined (ground speed). Just walking up regular stairs would be like an aircraft flying with no wind.
It can also happen in reverse. If you walked down the up escalator your walking speed (air speed) may be equal to the escalator. Your total speed (ground speed) may even be zero. Aircraft leaving London going to NY were fighting the wind their ground speed was reduced.