The area of Beersheba is first mentioned in The Bible as the place where Hagar went after she was sent away from Abraham because of family conflicts with Abraham's wife Sarah. Hagar was Abraham's Egyptian-born concubine who had a son (see Ishmael) by Abraham when Sarah thought that she herself was unable to have children. Then, when Sarah did have a son herself (see Isaac), she could no longer tolerate Hagar's presence, so she forced Hagar to leave. Abraham reluctantly agreed to Sarah's demand.
The actual well of Beersheba was apparently dug by Abraham's servants, and was a place of conflict when Abimelech's servants attempted to seize it. To preserve peace, Abraham and Abimelech made a treaty there in which the name of the town Well of Seven, with an extended meaning of Well of The Oath, was established (Genesis 21:31).
Other notable events of Beersheba: Jacob had his "stairway to heaven" dream in the area, and later God spoke to Jacob there when the Israelites were on their way to Egypt, where they would remain for over 400 years in eventual slavery before the Exodus (Genesis 46:1). The prophet Elijah sought refuge there after wicked Jezebel ordered him killed (1 Kings 19:3). Samuel's two corrupt sons, Hophni and Phinehas, who served as judges there caused the Israelites to demand their first king, which they got in Saul (1 Samuel 8:1-3, 9:1-2,17).
Fact Finder: In which area of the 12 tribes of Israel was Beersheba?
Joshua 19:1-2 and map above