A reinforcing piece of fabric sewn into a garment is called a gusset. Manufacturers use metal gussets to reinforce joists or join metal plates together.
Most gussets are shaped like triangles. Some gussets make clothing sturdier, and some make it wider or shape it more accurately to the body. They might be added along the sides of a shirt, under the arms, or at the spot where inside leg seams meet in a pair of pants or tights. The original gussets were used in chain mail or armor, to cover unprotected areas. The word comes from the Old French gosset, "armhole," or "piece of armor for the armpit."