Furriel is a fascinating and somewhat archaic word that literally means 'quartermaster' or 'orderly' in a military context. It refers to someone who manages provisions, lodging, or serves as an assistant.
In this song, the lyric "Tú, me tienes de furriel" (You have me as your orderly) is a poetic and unique way of expressing complete devotion and subservience. The singer is saying that the object of their affection has them completely at their beck and call, managing their every need, much like a military orderly. This unusual usage makes it very memorable and intriguing.