Pieces would be the remaining parts: the legs (consisting of the thigh and drumstick), the neck, the back, or the innards. No doubt these too will someday become fashionable, and Chicken Pieces will be reduced to meaning bags of plucked feathers.
You’ll have to figure out what Chicken Pieces are best to use based on the recipe you are looking at: if it looks like you are expected to end up with some meat, you’ll probably want the chicken legs. If it looks like the Chicken Pieces are just being boiled to make a flavourful water, then it’s too wasteful to use the legs: you’ll want necks or backs instead. The backs contain a lot of flavourful marrow for stock.