Cowboys are arnimal herders that tend to cattle. Cows are cattle. A calf is a baby cow. The plural of calf is calves. Calves can also refer to the muscle at the back of a person's leg below the knee. Branding is the act of marking another by burning their flesh with heat from an iron. This leaves the branded area sore. The joke is playing on the word calves and its different meanings. Calves, or the muscle beneath the knee, can get sore from exercise. Calves, the baby cows, are sore from getting branded. 
During branding cowboys have sore calves .