So the first part of this series explained heat index, a semi-useful way of quantifying the effect of humidity on the temperature your body perceives. Unfortunately heat index really only has any relevance when it's hot enough for you to be sweating, so to perform the same type of correction in cold weather we have to go to a different method, in this case the dreaded Wind Chill Factor.
The idea between wind chill is simple but thermodynamically kind of interesting. Basically, heat likes to diffuse into places where there's less heat; the bigger the difference in heat between the two places, the faster this diffusion occurs. Your body is continually dumping heat into the (much cooler) atmosphere around you via various mechanisms, which heats the air immediately around you. If you're standing in a totally wind-free area, that heated air around you will pretty much stay where it is, which means you're surrounded by air that's warmer than usual because of the heat you've been dumping into it. The warmer that air gets, the smaller the temperature difference between your body and the air gets, and as a result the rate at which your body can dump heat into the surrounding air slows. This can be quantified with a bunch of partial differential equations but I don't care and you don't care, so we'll stick with "conceptual explanation" for now.
There's a pretty easy way around this that you've probably already figured out: blow the hot air away. Anyone who's ever stood in front of a fan or blown on something to cool it off knows that stuff can dump heat faster when the air around it is being continually replaced by cool air before it can heat up too much. This can be all kinds of useful on hot days (see aforementioned fan), but when it's freezing cold and your body is desperately trying to hold onto all the heat it possibly can, waves of fresh, subzero air blowing over you will make it substantially harder than usual to keep warm (see handy illustration)
Enter the wind chill factor, yet another attempt to quantify the perceived effect of other factors (in this case the wind stealing all your heat) on the temperature you actually perceive. Like the heat index, the wind chill factor was created with the best of intentions (making sure school kids don't freeze to death at the bus stop and such), and also like the heat index it's now mainly used to make weather reports more dramatic-sounding.
There are actually several dueling schools of thought on how windchill should be calculated, because apparently people have time on their hands these days. The first experiment to measure the windchill was developed, probably out of necessity, by two dudes in the Arctic sometime before WWI. Basically they hung a bottle of water outside their tent or igloo or whatever next to a wind speed gauge, timed how long it took the bottle to freeze, and correlated that with how fast the wind was blowing. They used this data to calculate something called the Wind Chill Index, basically just a number that tells you how likely you are to freeze to death if you go outside. It's a pretty simple equation that I'm guessing is just a curve-fit to their data.
Because Americans are superstitious and distrustful of science and its fancy "units" and "equations," they were generally confused by the Wind Chill Index. Someone got it into their head to "solve" this problem by defining a wind chill equivalent temperature, which is what we used today. The first models used to calculate this were pretty dumb, and actually seem to have pissed off the dudes who invented the original Wind Chill Index quite a bit, but our current method (based on the heat loss of bare skin facing into wind of a given velocity) is slightly more sophisticated. It's still semi-empirical, only valid in certain temperature/wind speed ranges (in this case below 50F and above 3 mph), and operates under a lot of assumptions about clothing (hilariously, there is still some debate among wind chill experts as to whether the calculation should assume a naked dude or a dude wearing "appropriate clothing" in an open field. As in most cases, I am totally on the naked side here) and activity level and such, but it has familiar-looking units and gives at least a reasonable approximation of what you're walking into when you leave the house in January, so we'll take it, I guess.
If you like math and hate free time, Wikipedia has all the equations used to calculate this stuff, as well as most of the information I've cleverly paraphrased here.