Yin and yang refer to the qualities that arise as a result of differentiation. The art of Taijiquan can be understood as the pursuit of mastery over the practical effects of this differentiation throughout the body (whether for martial, health, or other purposes).
The assignment of yin or yang to a particular body part, quality, or object depends on the context of the differentiation. A piece of chalk can be yin because it is white and yang when it is being used to write. The outer surface of it is yang while its interior is yin. Throw a piece of chalk and it is yang while flying through the air and yin when it comes to rest.
One of the most important differentiations for our purposes (other than the most basic, which is between up and down) is between the free, active side (yang) and the braced, stable side (yin) as when engaged in santi stance, issuing power via fajin, or practicing xingyi. Since our perception of neutral is yang by default, finding true stability or neutrality requires constant focus and attention to actively introduce enough yin to balance our “default” yang.