Daenerys Targaryen and Jon Snow are cousins.
They share a common ancestor, Aegon the Conqueror, who founded the Targaryen dynasty. Daenerys is the daughter of Rhaegar Targaryen, who was the eldest son of Aerys II Targaryen. Jon Snow is the son of Lyanna Stark, who was secretly married to Rhaegar Targaryen.
Therefore, Daenerys and Jon are half-siblings through their father, Rhaegar.