There are at least two people in the Bible named Ishmael. The name is sometimes translated into English as Ishmail. The first and most famous was Ishmael, son of Abraham. Another was Ishmael, the son of Nethaniah, best known for killing Gedaliah, who had been appointed as governor of Judah.
Ishmael was the first son of Abraham. His mother was Hagar, who was the Egyptian handmaid to Sarah, who was Abraham's wife. Ishmael was the half-brother of Isaac, who was the son of Abraham and Sarah. Sarah had been unable to have children. So she presented her maid, Hagar, to Abraham to bear an heir for Abraham.
Hagar gave birth to Ishmael when Abraham was 86 years old. Fourteen years later, Isaac was born. When Isaac was weaned, Abraham gave a party to celebrate the occasion. But Sarah noticed that Ishmael teased Isaac, and she told Abraham to send away Hagar and Ishmael.
Abraham was upset, but the Lord told him to do as Sarah had requested, because Isaac was to be the heir of Abraham, to inherit the promises that God had made to Abraham and his offspring (Genesis 21:12-13).
Hagar and Ishmael left Abraham and lived in the wilderness of Paran. God blessed Ishmael and he became an expert archer, and his mother arranged a marriage for him with a girl from Egypt. Ishmael had twelve sons, and they became the founders of the twelve tribes that bore their names: Nebaioth, Kedar, Abdeel, Mibsam, Mishma, Dumah, Massa, Hadad, Tema, Jetur, Naphish and Kedmah. These tribes scattered across the land. Ishmael died at the age of 137.