Albert Barnes Commentary Numbers 10:33

"And they set forward from the mount of Jehovah three days` journey; and the ark of the covenant of Jehovah went before them three days` journey, to seek out a resting-place for them." — Numbers 10:33 (ASV)

Three days’ journey - This was probably a technical expression for a distance that could not be traversed in a single day, and therefore requiring intervals for encampment and due provision: compare Genesis 30:36; Exodus 3:18; Exodus 5:3; Exodus 8:27; Exodus 15:22. The technical use of the phrase “Sabbath-day’s journey” for another average distance (Acts 1:12) is similar.

The ark of the covenant of the Lord went before them - From Numbers 10:21; Numbers 2:17, it would appear that the usual place of the ark during the march was in the midst of the host. It was evidently an exceptional case when, in Joshua 3:3, Joshua 3:6, the ark preceded the people into the bed of the Jordan. Therefore, the words “went before them” do not here imply local precedence. The phrase, or its equivalent, is used of a leader going out in command of his troops (Numbers 27:17; Deuteronomy 31:3; 1 Samuel 18:16; 2 Chronicles 1:10); and similarly, the ark may well be said to have gone at the head of the Israelites, when it was borne solemnly in the midst of them as the outward embodiment of the presence whose sovereign word was their law.

A resting place - Literally, “rest.” It is commonly understood to refer to each successive encampment, or, in particular, to the first encampment. Yet the term would hardly be used here if it did not carry with it a higher meaning, pointing to the promised rest of Canaan, for which the Israelites were now in full march, and from whose speedy enjoyment no sentence of exclusion yet debarred them.