During the journeys of Israel the Ark of the Covenant was covered with a blue cloth to show that it was something heavenly.
One of the mysteries of the Ark of the Covenant was a question of why God commanded Moses to tell the Israelites that when they journeyed through the wilderness the Ark was to be covered with a blue cloth and then carried by the sons of Aaron. When they came to the border of the promised land at the Jordan River the waters parted before the Ark of the Covenant. But anyone watching would have seen that the Ark was covered in blue. The Bible mentions the color blue often in reference to heavenly things, for example the Ark of the Covenant was a revelation of God's plan of redemption through Jesus. Many things near the Ark of the Covenant had special heavenly meanings, from the alloys that were used in the construction of the tabernacle, to the Cherubim, and the four colors woven into the garments of the high priest, and the veil that separated the holy place from the holy of holies. Blue was a special color and spoke of something heavenly, something that was not of this earth, something that had come down from above. Jesus told Nicodemus a mystery, that He had descended from heaven, and that the only way for men to be saved was to be born again, or born from above.
John 3:31 "He who comes from above is above all; he who is of the earth is earthly and speaks of the earth. He who comes from heaven is above all."
Scripture mentioning the color Blue covering the Ark entirely:
Numbers 4:5-6 - "And when the camp setteth forward, Aaron shall come, and his sons, and they shall take down the covering vail, and cover the ark of testimony with it: And shall put thereon the covering of badgers' skins, and shall spread over it a cloth wholly of blue, and shall put in the staves thereof."
This exalted the Ark in contrast to all other furniture.
Some Scriptures mentioning the color Blue in the construction of the Tabernacle:
Exodus 26:1 - "Moreover you shall make the tabernacle with ten curtains of fine twisted linen and blueand purple and scarlet [material]; you shall make them with cherubim, the work of a skillful workman.
Exodus 26:31 - "And you shall make a veil of blue and purple and scarlet [material] and fine twisted linen; it shall be made with cherubim, the work of a skillful workman.
Exodus 26:36 - "And you shall make a screen for the doorway of the tent of blue and purple and scarlet [material] and fine twisted linen, the work of a weaver.
Exodus 28:6 - "They shall also make the ephod of gold, of blue and purple [and] scarlet [material] and fine twisted linen, the work of the skillful workman.
Exodus 28:15 - "And you shall make a breastpiece of judgment, the work of a skillful workman; like the work of the ephod you shall make it: of gold, of blue and purple and scarlet [material] and fine twisted linen you shall make it.
Exodus 28:28 - "And they shall bind the breastpiece by its rings to the rings of the ephod with a bluecord, that it may be on the skillfully woven band of the ephod, and that the breastpiece may not come loose from the ephod.
Exodus 28:31 - "And you shall make the robe of the ephod all of blue.
Exodus 28:33 - "And you shall make on its hem pomegranates of blue and purple and scarlet [material], all around on its hem, and bells of gold between them all around:
Exodus 28:37 - "And you shall fasten it on a blue cord, and it shall be on the turban; it shall be at the front of the turban.
1 Chronicles 15:14-15 "So the priests and the Levites consecrated themselves to bring up the ark of the LORD, the God of Israel. And the Levites carried the ark of God on their shoulders with the poles, as Moses had commanded according to the word of the LORD."