The gid hanasheh is the sciatic nerve

Sciatic nerve

The sciatic nerve is a large nerve fiber in humans and other animals. It begins in the lower back and runs through the buttock and down the lower limb...

 that may not be eaten by Jews according to Halacha (Jewish Law). The laws of prohibition regarding the gid hanasheh are found in Masechet Chullin (Hullin) Perek 7.

Source

The Torah

Torah

Torah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five books of the bible—Genesis , Exodus , Leviticus , Numbers and Deuteronomy Torah- A scroll containing the first five books of the BibleThe Torah , is name given by Jews to the first five...

 (Genesis, chapter 32) recounts that Jacob

Jacob

Jacob "heel" or "leg-puller"), also later known as Israel , as described in the Hebrew Bible, the Talmud, the New Testament and the Qur'an was the third patriarch of the Hebrew people with whom God made a covenant, and ancestor of the tribes of Israel, which were named after his descendants.In the...

 fought with an angel

Angel

Angels are mythical beings often depicted as messengers of God in the Hebrew and Christian Bibles along with the Quran. The English word angel is derived from the Greek ἄγγελος, a translation of in the Hebrew Bible ; a similar term, ملائكة , is used in the Qur'an...

 (according to Rashi

Rashi

Shlomo Yitzhaki , or in Latin Salomon Isaacides, and today generally known by the acronym Rashi , was a medieval French rabbi famed as the author of a comprehensive commentary on the Talmud, as well as a comprehensive commentary on the Tanakh...

 this was Esau

Esau

Esau , in the Hebrew Bible, is the oldest son of Isaac. He is mentioned in the Book of Genesis, and by the minor prophets, Obadiah and Malachi. The New Testament later references him in the Book of Romans and the Book of Hebrews....

's guardian angel) who could not beat him. At the end of the fight, the angel moves a nerve in Jacob's leg causing him to limp. The verse then states: "Therefore the children of Israel (Jacob) do not eat the gid hanasheh until today."

Removal

The removal of the gid hanasheh and cheilev (other forbidden fats) is called nikkur

Nikkur

Nikkur is the process of making an animal kosher by removing chelev and the gid hanasheh .It is much easier to perform nikkur on the front part of the animal...

. Since it is labor intensive to remove all the forbidden parts of the hind-quarters of an animal, the entire hind quarters are usually sold to the non-kosher market.