BMI, or Body Mass Index is a way to describe the body shape of people in a single number.
There are a few ways to describe a body shape. I prefer a combination of the height and weight. OKCupid prefers age and height. Sir Mix-a-lot perfers your bust, waist and hip measurements.
BMI uses a fairly simple calculation, combining figures for height and weight into one factor like this: BMI = weight/height^2.
It was invented by Adolphe Quetelet in the 1800s, so he could assign a value of thinness or fatness to any size of person (or population). It yeilds a fairly good spectrum of thin to obese bodies, regardless of height, but it isn't the perfect ratio. It is just a kind of shorthand way of calculating it.
Calculating BMI with either metric or American standard units will yield the same BMI.
Here's a spectrum of BMI measurements. These thumbnails are taken from the Photographic Height/Weight Chart. Please keep in mind that while BMI is often used to illustrate a population's health, but its calculation doesn't differentiate between muscle weight and fat weight.
Also, there are several possible heights for a given BMI, for example a 4'10 100 lbs. person shares 21 BMI with another person at 6'1 160 lbs. and a third at 6'8 190 lbs.