According to the Bible, Moab was the son of Lot, and therefore the nation of Moab was related to the Israelites (Genesis 19:30-38). The Moabites, who settled east of the Dead Sea (present day Jordan), had a highly developed culture, and artifacts written in Hebrew bearing Moabite inscriptions support the widely held view that the Moabites spoke the biblical language. During the Exodus period, part of the Moab kingdom was taken by the Amorites; Israel would later capture the territory. This parcel of land then became the object of contention and exacerbated animosity between the two nations. One example of the feud between the two nations is the story in the Torah of Balaam, who was sent by Moabite king Balak to curse the Jewish nation.
Sources: Bridger, David. Ed. The New Jewish Encyclopedia. NY: Behrman House, Inc. 1976.
Schreiber, Mordecai (ed.). The Shengold Jewish Encyclopedia. Shengold Books. 1998.
Telushkin, Joseph. Jewish Literacy. William Morrow and Company, Inc. 1991.