What does Mark 13:31 mean?

This is not as much a comment on the end times as an oath that what Jesus says is true. Jesus' truth is not transitory. It is not relative to time, place, or culture. Although He is primarily addressing Jews, the audience does not make the accuracy of His words relative.

In a more literal interpretation, heaven and earth will pass away. After the final battle at the end of the millennial kingdom, after Satan is thrown permanently into the lake of fire and unbelievers are judged at the great white throne (Revelation 20:7–15), God will destroy the corrupted heaven and earth and create a new place for His followers to live (Revelation 21:1). Even then, Jesus' words will stand true.

Non-Christians and believers alike tend to put confidence in worldly things. We build and landmark giant trees that have lived hundreds of years. We do the same with cities that have existed for millennia. We see mountains that haven't moved in human memory. We describe businesses like banks as "too big to fail." Even more transitory things like politicians and investment plans (Isaiah 40:8) are treated as reliable or trustworthy. But Jesus says all these earthly things will be destroyed. They are not worth our trust compared to Jesus' words. Only His words bring true, everlasting life.