Chickens are not mammals, so they don't have breasts, per se. Chickens don't have nuggets or fingers either, but that's a story for a different day.
Chickens, as well as other fowl, have a chest area that is referred to as the breast, I guess because chicken breast sounds sexier than chicken chest. Each chest area consists of two pieces of meat, sort of like a human's pectoral muscles, separated by the breast bone. When you cut up a chicken into pieces, each piece of meat on either side of the breast bone is referred to a a breast half. Sometimes you can find the entire breast, with the breast bone and ribs intact, but they don't come skinless, and they are obviously not boneless.
In order to confuse new cooks even more, some recipes will call for cutting each breast half in half crosswise. This is done to create eight equal sized pieces, which will cook more evenly