Genesis 32 records Jacob wrestling through the night before his meeting with Esau. He was given the name Israel, and his descendants subsequently became known as the children of Israel.
During the Exodus, Israel became the principal biblical designation for the people whom God delivered from Egypt and with whom He established the covenant at Sinai. After the conquest and settlement of Canaan, the tribes formed the nation over which Saul, David, and Solomon ruled.
Following Solomon's death, the kingdom divided. Ten northern tribes followed Jeroboam I and were generally called Israel, while Judah and Benjamin remained under the Davidic dynasty. The northern kingdom existed until the Assyrian conquest in the eighth century BC.
The prophets continued to use the name Israel in theological as well as political senses, particularly when speaking about God's covenant, judgment, restoration, and promises concerning His people.