The war with Sihon and Og is an important one in the story of the Exodus and you will find it referenced many times in the Old Testament.
What made these conquests so significant?
The area to the east of the Jordan was area occupied by the Moabites and the Ammonites, descendants of Lot. God had given this land to these people and forbidden Israel to take any of it for themselves.
But over the years, the Canaanites (also called “Amorites”) had conquered much of that land and had settled it with fortified cities all the way into Bashan in the north and to the east of the Sea of Galilee. Originally, none of this land could have been used by Israel. It had been given by God to someone else. But because the Moabites and the Ammonites had not secured it for themselves, it became fair game for Israel.
The defeat of the Amorite kings Sihon and Og constituted the beginning assurance that Israel would indeed conquer the land of Canaan. Why not? They had conquered two extensive Canaanite kingdoms and one of the kings was Og, a giant of a man who was the last of the Rephaim, a name given to the giant people east of the Jordan. These people were called the Anakim on the west side of the Jordan (Deuteronomy 2:11) and fear of them is what kept Israel from entering Canaan the first time (Numbers 13:26ff). That Israel has now utterly defeated these people was supposed to be an encouragement to Israel to press on and enter Canaan and begin the work of driving out (or killing) the Canaanites.
Israel should have gone forward in the strength of the Lord and done everything God told her to do. But she doesn’t. One gets the feeling that it is not because she cannot, but that she becomes distracted, more interested in pursuing her own goals than pursuing God’s. And when that happens, failure becomes her lot.