@Superdesk has the right answer, but I thought I'd add some math to give an impression of the size of the difference.
As others have stated, drag is a quadratic function of relative wind speed. This is why you need a lot more effort to go from 0 to 10 km/h than from 20 to 30 km/h on a bike.
Suppose that you like to bike at 20km/h. If you go for a ride on a day with no wind, you have a relative wind speed of 20km/h the whole way (you move 20 km/h faster than the air around you). Suppose that you lose 1000 Cal. to drag on this ride.
Now suppose you go riding on a day with a 10 km/h wind, and ride a loop that's half as long.
For the first half of the loop, with a tail wind, your relative wind speed is 20-10 km/h = 10 km/h. But because drag is quadratic, this means you actually lose just one fourth the energy you would at a 20km/h wind speed. So you lose 125 Cal to drag on the first half of the ride (1000/2 = 500 for only riding half way, 500/4 because of the reduced drag).
On the second half of the loop, with a head wind, your relative wind speed is 20+10 = 30 km/h. Again, because drag is quadratic, this means you don't expend 50% more energy, you expend 125% more energy. So you lose 1125 Cal. to drag on the second half of the ride (1000/2 = 500 for only riding half way, 500 *9/4 = 1125 for the quadratic drag)
So in total on the windy day, you expend 1250 Cal, or 25% more riding the same distance, at the same ground speed, just for a light breeze! Also interesting to note that you'll lose 90% of the energy on the way back!
This actually gets worse very fast as the wind speed climbs. Where I live we often have 40km/h sustained winds, which means 450% more energy loss for the same ground speeds. This is when it takes all your energy to ride downhill!