The ESV Study Bible says this about our passage in Numbers today (Chapters 3-4)
This chapter again shows preparations being made for the march into Canaan. It underlines once again the dangerous holiness of God: he cannot be approached casually. It also emphasizes the importance of the ministry of the Levites, who make possible the transport of the tabernacle to the land and who guard it from intrusion.
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Relationship to the New Testament
Interesting to note is 1 Corinthian’s use of Numbers. Paul says in two places that Israel’s disobedience was to serve as an example of “warnings” or what not to do (10:6, 11). He then relates these issues to dealing with temptation, noting that “God is faithful; he will not let you be tempted beyond what you can bear. But when you are tempted, he will also provide a way out so that you can stand up under it,” (10:13).
Furthermore, Hebrews 3:7 – 4:11 also deals with Israel’s disobedience. More specifically it quotes Psalms 95:7-11, although this passage also deals with the events in the book of Numbers. The author of Hebrews warns its readers of unbelief, using Israel as an example. He encourages them to “take care” lest they have “an evil, unbelieving heart that turns away from the living God” like the Israelites of old (Heb. 3:12). In the end, after using Israel as an example, the writer of Hebrews exhorts his readers: “Let us therefore make every effort to enter that rest, so that no one may fall through such disobedience as theirs,” (Heb. 4:11).