Albert Barnes Commentary Numbers 1:1-4

"And Jehovah spake unto Moses in the wilderness of Sinai, in the tent of meeting, on the first day of the second month, in the second year after they were come out of the land of Egypt, saying, Take ye the sum of all the congregation of the children of Israel, by their families, by their fathers` houses, according to the number of the names, every male, by their polls; from twenty years old and upward, all that are able to go forth to war in Israel, thou and Aaron shall number them by their hosts. And with you there shall be a man of every tribe; every one head of his fathers` house." — Numbers 1:1-4 (ASV)

A month had passed since the tabernacle was set up (Exodus 40:2, Exodus 40:17), and the Sinaitic legislation was now complete .

A census (“sum”) was commanded, based not on any new registration of individuals, but on what had accompanied the previous collection of offerings (compare Exodus 30:11 and following; Exodus 38:25–28). The offerings had probably been tendered by the people in groups. If certificates of registration were furnished to such groups, the new census could be easily carried out using these documents and completed (Numbers 1:18) in a single day.

This registration enrolled persons after their families, by the house of their fathers; and was superintended not by the Levites (see Exodus 38:21 and note), but by an assessor for each tribe (Numbers 1:4), who was to act with Moses and Aaron in this business. The purpose of this census was not only religious; it would also serve as a basis for various civil and military arrangements.