This verse describes a specific part of the Israelites' marching order during their journey through the wilderness. Let's break it down:

"The Kohathites set forward, bearing the sanctuary." The Kohathites were a specific family (clan) within the tribe of Levi. They had the special responsibility of carrying the most sacred objects of the Tabernacle, including:
The Ark of the Covenant (containing the Ten Commandments)
The Table of Showbread
The Golden Lampstand (Menorah)
The Altars

Because these objects were considered extremely holy, they were covered with special cloths and carried on poles to protect them from direct touch. The Kohathites went ahead of the other groups.

"The others set up the tabernacle before they arrived." "The others" refers to other groups of Levites. These groups were responsible for transporting and setting up the Tabernacle itself: the tent structure, its curtains, framework, and other components. This verse means that these groups would travel behind the Kohathites. When the Kohathites reached the designated place to stop, the rest of the Levites would have already been at work setting up the Tabernacle. This ensured that a place was ready to house the most holy objects the Kohathites were carrying.

In summary:

The verse describes a coordinated effort where the Kohathites, carrying the most sacred objects, were followed by other Levites who were responsible for assembling the Tabernacle structure. This ensures the Kohathites would arrive to a sanctuary already prepared for them.
This demonstrates:

Order and precision: The Israelites' movements were carefully planned and executed according to God's instructions.
Respect for the holy: The sacred objects were given priority and protection. The Tabernacle was prepared in advance to receive them.
Division of labor: Different groups had specific responsibilities, ensuring efficient and organized movement.