The names of the twins in the bible are Jacob and Esau. They are the sons of Isaac, son of Abraham, and his wife Rebekah. There is another set of twins as well, Pharez and Zarah, born to Judah and Tamar.
In Genesis 25:23, God tells Rebekah that she is pregnant with twins, and that the older one will serve the younger. When she gives birth in the next verse, Rebekah does indeed have twins. The first is named Esau and the second Jacob. Esau grows to be a hunter, while Jacob grows to be a peaceful man who prefers to live in tents. Isaac preferred Esau, while Rebekah favoured Jacob, which leads to Jacob essentially stealing Isaac's blessing as he lay dying.
This theft raises Jacob to the head of the family, instead of Esau. Jacob goes on to become Israel, the father of many children. Among them is Joseph, who is sold into slavery in Egypt by his brothers, and Judah, who becomes the father of the twins Pharez and Zarah. The 12 tribes of Israel are descended from these many sons of Jacob.