Gid Hanasheh

At the root of this mitzva lies the purpose that the Jewish people should have a hint that even though they will endure great tribulations in their exiles at the hands of the nations and the descendants of Esav, they should remain assured that they will not perish, but their offspring and name will endure forever, and a redeemer will come and deliver them from the oppressor's hand. Remembering this matter always through this mitzvah, which will serve as a reminder, they will stand firm in their emuna and righteousness forever.

(Sefer HaChinuch)