gusset; crotch piece
A piece of fabric inserted into a garment to add room or shape, especially in the crotch of pants or underarms. Common in sewing and tailoring contexts.
These pants have a gusset, so they're easy to move in.
Inserting a gusset under the sleeve makes it easier to raise your arm.
Hiragana spelling, also used.
The origin is uncertain; the word is native Japanese and the kanji 襠 is a specialized character for this meaning.