Watts per kilogram (W/kg) is a way to normalize a cyclist's power output, Watts (W), by their weight in Kilo-grams (kg).
Training Peaks has an excellent article on why you should focus on Watts per Kilogram:
"For the cyclist that rides on completely flat roads or trails, W/kg isn’t very important. If the terrain is flat, then the rider with the highest absolute power will almost always go faster. However, for athletes that ride regularly in hilly terrain, compete in events with climbs, or want to be more proficient sprinters, W/kg should be a primary focus. Unlike many of the other metrics cyclists track, W/kg is relatively straightforward to improve. There are only three ways in which you can affect some change in your W/kg. They are as follows:
Increase your power output while keeping your weight constant.
Keep your power output constant while decreasing your weight.
Increase your power output while also decreasing your weight."