This name applies in the Bible to the people of Israel, who were referred to as Israelites, Hebrews, or Jews.
The key idea in the Old Testament is that God chose Israel (the descendants of Abraham) to be the recipients of His moral and spiritual guidance.
The idea is expressed many times in the Bible, notably in Deuteronomy 7:6: “You are a holy people to the LORD your God; the LORD your God has chosen you to be a people for Himself, a special treasure above all the peoples on the face of the earth.”
(This is similar to the idea Americans have that we are a “special” nation dedicated to freedom and equality.)
The Bible makes it clear that the “chosen people” are never to be arrogant or cocky because God has chosen them.
In fact, because God revealed Himself and His moral law to Israel, the people of Israel will be severely punished when they break the moral law. Being “chosen” was a privilege but also an obligation.
See 632 (covenant); 274 (Israelites).