The way we talk about paper in the United States is amazingly convoluted. The short answer is that 500 sheets of bond paper with a size of 17" by 22" have a weight of 20 pounds. The manufacturer would cut a sheet that big into four letter-size sheets, so a 500-sheet ream of 20-pound bond paper weighs 5 pounds.
If it was something other than bond paper, then the size of the standard sheet used to determine the weight might be different. For example, Bristol paper is heavier and stiffer (like the paper in a manila file folder). Its standard sheet size is 22.5" by 28.5".
In general, the more a sheet of a certain grade of paper weighs, the thicker it is. You can purchase 20-pound and 24-pound bond paper at an office supply store. The 24-pound bond paper is thicker, heavier and more opaque than 20-pound bond.
The metric system has a much better way of measuring paper. A0 paper is a square meter of paper. One side is 84.1 centimeters long and the other is 118.9 centimeters (the longer side's length is the square root of 2 longer than the shorter side's length). A1 paper is half of an A0 sheet (preserving the square root of 2 rule). A2 is half of an A1 sheet, and so on. And paper weight is measured in grams per square meter, so it is very easy to figure out.