Avoirdupois is a system of measuring weight based on the fact that sixteen ounces are in a pound. The metric system is based on grams, and the avoirdupois system is based on pounds.
This odd-looking term means something very common, at least if you live in England or the United States: the avoirdupois system is a standard for measuring weight based on there being sixteen ounces in a pound. If you measure your weight in pounds, you're using the avoirdupois system. If you measure liquids in ounces, you're using the avoirdupois system. This is one of many standards of measurement that exist, such as the metric system, which is based on units of 10.