The Moabite language is an extinct Hebrew Canaanite dialect, spoken in Moab (modern-day northwestern Jordan) in the early first millennium BC. Most of our knowledge about Moabite comes from the Mesha Stele, as well as the El-Kerak Stela (http://www.kchanson.com/ANCDOCS/westsem/elkerak.html); this is sufficient to show that it was extremely similar to Biblical Hebrew, despite a few differences. The main differences noted, in the admittedly short text, are: a plural in -în rather than -îm (eg mlkn "kings" for Biblical Hebrew məlākîm), like Aramaic and Arabic; retention of the feminine ending -at which Biblical Hebrew reduces to -āh (eg qryt "town", Biblical Hebrew qiryāh); and retention of a verb form with infixed -t-, also found in Arabic and Akkadian (w-’ltḥm "I began to fight", from the root lḥm.)
The Moabites were a historical people, whose existence is attested to by numerous archeological findings, most notably the Mesha Stele, which describes the Moabite victory over an unnamed son of King Omri Israel (see 2 Kings 3).
The conflict between the Israelites and the Moabites is expressed in the biblical narrative describing the Moabites' incestuous origins.
Another Moabite king, Muẓuri ("the Egyptian" ?), is mentioned as one of the subject princes at the courts of Esarhaddon and Assurbanipal, while Kaasḥalta, possibly his successor, is named on cylinder B of Assurbanipal.
The Moabites were of Semitic stock and of kin to the Hebrews, as is indicated by their descent from Lot, the nephew of Abraham (Genesis 19:30-37), and by their language which is practically the same as the Hebrew.
Bands of Moabites ventured to raid the land of Israel when weakened by the conflict with Hazael (2 Kings 13:20), but Moab was probably subdued again by Jeroboam II (2 Kings 14:25), which may be the disaster to Moab recounted in Isaiah 15.
The Moabites lost their identity as a nation and were afterward confounded with the Arabs, as we see in the statement of Josephus (XIII, xiii, 5), where he says that Alexander (Janneus) overcame the Arabians, such as the Moabites and the Gileadites.