In Los Angeles we didn't have to worry about such things, but here in Missouri I've had to quickly learn about wind chill and the heat index. No one had ever been able to give me a concrete definition of either term, so I turned to the ever-reliable Wikipedia for answers.
Wind chill is the apparent temperature felt on exposed skin due to the combination of air temperature and wind speed. Except at higher temperatures, where wind chill is considered less important, the wind chill temperature (often incorrectly called the "wind chill factor") is always lower than the air temperature, because any wind increases the rate at which moisture evaporates from the skin and carries heat away from the body. The phase change of water (in sweat) from liquid to vapor requires that the molecules reach a higher energy state. That energy is acquired by absorbing heat from surrounding tissue by conduction (see heat transfer).
Because wind chill is related to evaporation, dry inanimate objects are not affected by wind chill the way humans and animals are. Wind chill won't have much effect on your car, house, or outdoor machinery.
Similarly, the heat index is a measure of how much the ambient humidity is affecting evaporation.
The Heat index (HI) is an index that combines air temperature and relative humidity to determine an apparent temperature — how hot it actually feels. The human body normally cools itself by perspiration, or sweating, in which the water in the sweat evaporates and carries heat away from the body. However, when the relative humidity is high, the evaporation rate of water is reduced. This means heat is removed from the body at a lower rate, causing it to retain more heat than it would in dry air. Measurements have been taken based on subjective descriptions of how hot subjects feel for a given temperature and humidity, allowing an index to be made which corresponds a temperature and humidity combination to a higher temperature in dry air.
Humid air slows the evaporation of sweat and thereby reduces our ability to cool ourselves. Simple enough! Both pages have common formulas for calculating these values, if you're feeling adventurous.