This passage of scripture and preceding chapters explain the duties of the clans of the Levite tribe with relation to the Tabernacle. God had set this tribe apart as the caretakers of the Tabernacle and they were to disassemble, transport and reassemble the Tabernacle at the command of God and under the direction of Aaron and his sons, the priests.
We find that the other eleven tribes have made an offering of carts and oxen with which the Levites are to transport the different components of the Tabernacle. These oxcarts were distributed by Moses to the Gershonite and Merarite clans. But Moses, under God's direction, held back the oxcarts from the Kohathite clan. Why? Because in verse nine we see that they are to bear the holy things of the Tabernacle directly on their shoulders. The most blessed clan of the Levites who were to be responsible for transporting the holiest of objects, also had the most difficult job to do. Yet even with their special calling, if they drew near the holy things before the priests had properly prepared them for transport, they would be struck dead.
How joyous that our Saviour has saved us from this physical toil and mortal fear. We have that new covenant in His blood, yet we still have a responsibility to take up our cross daily and follow Him. (Luke 14:25-27). That is our Kohathite Burden. We walk daily with Him in our hearts and with the Holy Spirit as our guide just as the Israelites followed the pillar of cloud. The "burden" is that He charges us to not hide our light under a cover, but to let it shine for all to see. (Matthew 5:15) As much as that light shines for others to see, it also reveals the truth about us.
Thankfully, in His infinite mercy, Jesus even offers to help us with this.
28"Come to me, all you who are weary and burdened, and I will give you rest. 29Take my yoke upon you and learn from me, for I am gentle and humble in heart, and you will find rest for your souls. 30For my yoke is easy and my burden is light." Matthew 11:28-30