The cities of refuge were to be six, three beyond the Jordan and three in the land of Canaan (vv. 13-14).
The number six signifies man, who was created by God on the sixth day (Gen. 1:26-27, 31), making mistakes.
The number three signifies the Triune God as the refuge for the man who makes mistakes. God regards us as those who make mistakes, and He has ordained that there be a refuge into which we may flee.
The number two (the two sets of three cities each) signifies a testimony standing in the universe.
The cities of refuge were to be not only for the sons of Israel but also for the strangers and sojourners among them (Num. 35:15). This signifies that the Triune God as the refuge for the mistake-making man is for all mankind. Today we all, both Jews and Gentiles alike, have a refuge, a place of protection, in the Triune God.
The cities of refuge were not for those who killed with an intent (vv. 16-21). Adam sinned without intent, and we, the descendents of Adam, have sinned in the same way. Our sinning today is foolish and nonsensical. Therefore, in the sight of God, we are those who sin without intent, and He considers our sinning as being without intent.
The cities of refuge were only for the one who killed a man without an intent, that he might be free from the hand of the avenger of blood, under the judgment of the assembly (vv. 22-25a). This means that the one who fled to a city of refuge was not judged immediately. Rather, the assembly, the congregation, was to have a group to judge whether or not one's fleeing to the city of refuge was legitimate.