Answer: The Ark of the Covenant, built under God's direction (Exodus 25), was the holiest physical object within the Tabernacle's (later the Temple's) most sacred location known as the Holy of Holies.
The Ark of God, which symbolized His presence and glory, contained within it a pot of manna, Aaron's budded rod, and stone tablets inscribed with the Ten Commandments (Exodus 34:28, Hebrews 9:4). It existed as an Israelite possession from the time of Moses until Jerusalem was attacked by Babylon's King Nebuchadnezzar.
It was prophesied, 100+ years before the temple's destruction, that all its treasures would be taken to Babylon (2Kings 20:17). This was accomplished during Nebuchadnezzar's three attacks on Jerusalem (2Chronicles 36:7, 10, 18). It is during Babylon's third attack, in 586 B.C., that the city and its "house of prayer" (Matthew 21:13) is burned to the ground.
The Ark of the Covenant, once taken to Babylon, existed for an unknown period of time before likely being lost or possibly cut into pieces (see 2Kings 24:13) and its precious materials reused for other purposes.
It should be noted that the Ark is not mentioned as one of the treasures given back to captive Jews when they were allowed to rebuild the temple (Ezra 1:7 as well as chapters 5 - 6). The Ark of God was still missing, roughly 500 years later, when Herod the Great began to tear down and rebuild the temple. In its place, within the Holy of Holies, was a large stone on which the high priest sprinkled blood on the Day of Atonement (The Temple its Ministry and Service at time of Christ by Alfred Edersheim, Chapter 2).
We find an interesting statement in Jeremiah which declares that the ark and all that is with it will not be important during the Millennium (Jeremiah 3:16). What will be important will be the New Covenant God will offer all humanity. The book of Hebrews, chapter 9, explains that the spiritual or holy relics found in Jerusalem's Temple were mere patterns or copies of spiritual realities in heaven (Hebrews 9:1 - 5, 23 - 24).
Amazingly, Revelation 11 states that the Ark of the Covenant will be seen again in the near future. It will appear in the third heaven, the place where God's throne resides, after an angel loudly declares that the Lord is coming back to earth to rule all humanity (Revelation 11:15, 19)! It is not the physical object once found in the temple and transported to heaven but rather is the original one composed of spirit essence.