Body Mass Index, or BMI is a quick and easy way to determine whether you are overweight, obese, or healthy. It is a simple indicator that compares your height and weight to what is healthy. One thing to note is that this is (in my estimation) a crude method of determining your ideal weight, as it does not take into account different body types, though it could also be argued that the myth of different body types is simply and excuse for maintaining an inappropriate weight. Hm, I'm going to have to look up info on body types now...
According to the US Dept of Health and Human Services's Heart, Lung, and Blood Institute, BMI of less than 18.5 is underweight, 18.5 to 24.9 is healthy, 25 to 29.9 is overweight, and greater than 30 is considered obese. If you just want to determine what weight is healthy for your height, their handy-dandy table is a good resource for that. (It's worth noting that the table is more crude than the calculator, with one less decimal place.)
For example, a person with a typical woman's height of 5'4" should weigh no more than 140 lbs to be healthy, and would be considered obese at around 175 lbs. A person at a typical man's height of 5'11" should weigh no more than 180 lbs to be healthy, and would be considered obese at around 215 lbs. The AP (CNN) suggests that surgery, such as stomach stapling and other gross things, not be considered until a BMI of 40 (around 235 lbs in the average woman or 285 lbs in the average man). This can be reduced to a BMI of 35 (205/250 lbs) if there are other "weight-related medical problem(s) like diabetes or high blood pressure." (AP/CNN)
I am glad to say that I am on the underweight edge of healthy, at a BMI of 19. My mother has Type II diabetes, and I suspect is at least overweight, if not obese, but I don't actually know her weight. I do know that she doesn't appropriately monitor her diet or ever exercise, and she probably needs to increase her insulin dose, but she is still in denial about it all (some 4-ish years after first diagnosis). Sad.