Abbreviation of 'kagaku-sen'i' (chemical fiber); refers to synthetic fibers (man-made fibers) commonly used in clothing and textiles.
このコートは化繊で軽くて暖かい。
This coat is made of synthetic fiber; it's light and warm.
化繊のシャツは速乾性が高いものが多い。
Many synthetic-fiber shirts are quick-drying.
ラベルに『化繊』と書いてあれば、化学繊維（化学繊維）が使われているということだ。
If the label says '化繊', it means chemical/synthetic fibers are used.