The Egyptians have always liked pairs, either contrasting or complementing each other. They even would look at their own country as consisting of two parts (Upper- and Lower Egypt, the two riverbanks, the two lands).
Similarly gods were often paired and it is not always clear whether or not the second of the two had its own role as a god or was simply there to complement the first one. Many goddesses seem to have been just a female counterpart, like the goddesses that belonged to the Ogdoad of Hermopolis (Hauhet, Naunet, Kauket and Amaunet, paired with Heh, Nun, Kek and Amun, gods whose function is much clearer). In the same way Nephthys was usually paired with Isis (although her role may have been much more important), and similarly Tefnut was the counterpart of Shu.
Tefnut’s role, other than being the partner of Shu, is not quite clear. She is called goddess of moisture (being created by spitting), but the same applies to Shu. Both gods are mentioned together as lions in the Old Kingdom Pyramid Texts, as the eyes of the sky falcon (Shu usually being the sun and Tefnut the moon), and in Graeco-Roman times as the sign of twins in the zodiac.