The Moabites were a historical people. Their existence is attested to by numerous archeological findings, most notably the Mesha Stele, which describes the Moabite victory over Omri king of Israel (see 2 Kings 3).
The conflict between the Israelites and the Moabites is expressed in the biblical narrative describing the Moabites' incestuous origins. According to the story, Moab was the son of Abraham's nephew Lot, through his eldest daughter, with whom he had a child after the destruction of Sodom. The Bible then explains the etymology of Moab as meaning "of his father".
The following is a summary of the Biblical account, and may not correspond to actual historical events.
The Moabites first inhabited the rich highlands at the eastern side of the chasm of the Dead Sea, extending as far north as the mountain of Gilead, from which country they expelled the Emims, the original inhabitants, (Deuteronomy 2:11) but they themselves were afterward driven southward by the warlike Amorites, who had crossed the river Jordan, and were confined to the country south of the river Arnon, which formed their northern boundary. (Numbers 21:13; Judges 11:18)
The territory occupied by Moab at the period of its greatest extent, before the invasion of the Amorites, divided itself naturally into three distinct and independent portions:
The story of Ruth, on the other hand, testifies to the existence of a friendly intercourse between Moab and Bethlehem, one of the towns of Judah.
By his descent from Ruth, David may be said to have had Moabite blood in his veins. He committed his parents to the protection of the king of Moab, when hard pressed by Saul. (1 Samuel 22:3,4) But here all friendly relations stop forever. The next time the name is mentioned is in the account of David's war, who made the Moabites tributary (2 Samuel 8:2; 1 Chronicles 18:2). At the disruption of the kingdom, Moab seems to have absorbed into the northern realm.
At the death of Ahab the Moabites refused to pay tribute and asserted their independence, making war upon the kingdom of Judah. (2 Chronicles 22:1)
As a consequence of these events, Israel, Judah and Edom united in an attack on Moab, resulting in the complete overthrow of the Moabites. Falling back into their own country, they were followed and their cities and farms destroyed. Finally, shut up within the walls of his own capital, the king, Mesha, in the sight of the thousands who covered the sides of that vast amphitheater, killed and burnt his child as a propitiatory sacrifice to the gods of his country. Isaiah (15, 16, 25:10-12) predicts the utter annihilation of the Moabites; and they are frequently denounced by the subsequent prophets.
The public domain Smith's Bible Dictionary, found here