Okay, here it is as Chris explained it to me. Fluid drag force (air is a fluid—it takes the shape of its container) is proportional to velocity squared. Factors include the density of the fluid (so air is not as dense as water, for example); the drag coefficient of the object (bike, your clothing, etc.), the projected area in direction of motion (that’s why you get aero, to decrease your area), and velocity.

The drag force increases as the square of the wind velocity relative to the bike. Downwind, you subtract your speed from the wind speed. Upwind, you add your speed to the wind speed. So, for example, you have a 15 mph wind and your bike is going 10 mph. Downwind, the push you get is proportional to (15-10) squared = 25. Upwind, the resistance is proportional to (15+10) squared = 625. Fun, eh? Thanks to my cool engineer spouse for the explanation.