Moab was the son of Lot with his eldest daughter, shortly after the judgement on Sodom and Gomorrah (Genesis 19:30-38) and after Lot's daughters had gotten him drunk. This story is recounted in the book of Genesis in the Bible. His brother Ammon was born the same way to the younger daughter. Moab is the father of the Moabites, who lived on the east side of the Salt Sea (Dead Sea), in present-day Jordan.
Other meanings of Moab
The MOAB (Massive Ordinance Air Burst or "Mother of All Bombs") was a weapon developed by the U.S. Air Force prior to the Iraq War as part of the planned "shock and awe" strategy.
Moab is also the name of a town in Utah.