In more detail
The formula used in the US and Canada since 2001 is 35.74 + 0.6215T − 35.75V^0.16 + 0.4275TV^0.16, with T in °F and V in mph; the metric form is 13.12 + 0.6215T − 11.37V^0.16 + 0.3965TV^0.16, with T in °C and V in km/h. It models heat loss from a human face walking into the wind and applies only at or below 50 °F (10 °C) with wind of at least 3 mph (4.8 km/h).
Why it matters
The lower the wind chill, the faster exposed skin can freeze; at very low values frostbite can set in within minutes, so cover the face and hands. Wind chill applies to people and animals, not objects: wind cools a car engine or water pipe faster, but never below the actual air temperature, so water will not freeze in a 2 °C wind however strong it blows.
Example
20 °F, 15 mph wind → feels like 6.2 °F
0 °F, 30 mph → feels like −25.9 °F
−10 °C, 30 km/h → feels like −19.5 °C
−20 °C, 40 km/h → feels like −34.1 °C
Common confusion
Wind chill is the cold-weather counterpart of the Heat index; neither changes the temperature a thermometer reads.