Xanthe's Excavations are court activities at dig sites where the boyar Xanthe's people hunt for relics. Each one ends in a boss fight, and clearing them raises Xanthe's anger toward her boss quest.
Find the dig site, fight through it and kill the boss in the last chamber. Grab the note to finish. Unsealed Secrets ends with a Barrow Lord, Malevolent Presence in Tantari Woods with a Frenzied Soul.
Every court activity you finish raises Xanthe's anger. Fill it and you unlock The Cycle of Love, where you face her. Her activities stay open even after she is dealt with.