The Tertiary Winding is a winding which is present in large three phase transformers. The Tertiary Winding is delta connected. It is usually not connected to any load. The function of the Tertiary Winding is to provide a path for zero sequence curents which may flow in the event of an earth fault.
In Star-star transformers, the zero sequence current will not have a path through which it can flow. This can result in the current flowing through the tank walls causing the paint to peel off. The tertiary winding provides a circulating path for this current.
Tertiary Winding also provides a path for harmonics and helps in their mitigation.
Transformers with Tertiary winding are sometimes called Three winding Transformers.