What does Luke 21:33 mean?

Jesus has given several prophecies, including experiences the entire world will face before His return (Luke 21:8–11). He also mentioned persecution which His disciples will see in the following decades (Luke 21:12–19). He predicted the fall of Jerusalem and the temple in AD 70 (Luke 21:20–24), and the supernatural signs of the tribulation which will precede His return (Luke 21:25–28). Now, He promises that what He has said will happen. God's creation will cease to exist before His prophecies fail.

He has used similar wording before. When expressing the importance of God's law, He said, "But it is easier for heaven and earth to pass away than for one dot of the Law to become void" (Luke 16:17). The Old Testament has a similar sentiment: "The grass withers, the flower fades, but the word of our God will stand forever" (Isaiah 40:8).

Jesus' words here, paralleled in Matthew 24:35 and Mark 13:31, are stronger in their comparison. Heaven and earth will pass away. Second Peter 3:10 says, "But the day of the Lord will come like a thief, and then the heavens will pass away with a roar, and the heavenly bodies will be burned up and dissolved, and the earth and the works that are done on it will be exposed." Revelation 21:1 says, "Then I saw a new heaven and a new earth, for the first heaven and the first earth had passed away, and the sea was no more."

The meaning of the verse isn't to predict the destruction of the heavens and earth. The point is that ultimate truth—represented by Jesus' words—are more sure than the heavens and earth. As a side discussion, in the context of the chapter, His oath has interesting repercussions. The disciples began worried about the temple. Jesus warned them about earthquakes, war, persecution, and the disturbance of angels and demons. But the heavens and earth will be destroyed! That certainly adds some interesting perspective.