Simply put, the nose chain is a link between a nose piercing and an ear piercing. Typically, these "chains" are just that: chain links, usually (though not always) made of some kind of metal. Yet, besides actual chains, the term "nose chain" can denote other types of connecting materials between nose and ear piercings, such as the common alternative of rosary beads. Other connectors can be used as well.
The nose chain has been commonly worn by women in South Asia for centuries. Women in India have been wearing them since the 16th century when Mughal emperors brought them from Central Asia. It is especially significant during wedding ceremonies. Hindu tradition dictates that on the wedding night, the bride wears a nose chain, which is hooked by a chain to either the earring or hair. The bridegroom removes the nose chain, symbolizing the end of the bride's virginity.