The aircraft's velocity and inertia is referenced to the earth, not to the air through which it is moving. When the wind velocity changes, its force against the aircraft changes. This force produces an acceleration. If the aircraft's mass is large, it takes a while for this force to effect an acceleration on the aircraft. This is
why airliners are more prone to windshear related incidents than are light aircraft.
Imagine a goldfish swimming around in a large glass bowl. You pick the bowl up and carry it across the room. The goldfish doesn't notice that his 'groundspeed' has changed because his inertia is too tiny and the water just carries him with it. Now imagine a large ball bearing in the same bowl. This time, when you move the bowl, the ball bearing lags behind and tries to maintan its previous groundspeed, because it has greater inertia.
Aircraft are just huge fish swimming in an ocean of air. As the ocean moves across the ground (wind) they get carried along with it. But when the wind changes quickly, they try to maintain their previous groundpeeds.