What does Luke 20:33 mean?

This verse is the point where members of the Sadducee faction spring their philosophical trap on Jesus. He is on the Temple Mount, teaching His disciples and whomever else wants to listen. Religious leaders have been throwing out questions, trying to show the crowd that His teaching is wrong and the people shouldn't follow Him. First, they asked about who gave Him authority. He countered by threatening to reveal their sharp disagreement with the common people (Luke 20:1–8). Next, they asked Him if they should pay taxes to Caesar. He told them they should honor both Caesar and God (Luke 20:19–26).

The Sadducees continue the pattern of attempting to discredit Jesus without understanding potential flaws in their own argument. They tell a story about a woman whose husband died with no children. Following levirate marriage laws (Deuteronomy 25:5–6), she marries his brother to hopefully have a child who can inherit her first husband's birthright. The brother dies, as well. So, she marries the next. And then the next. In all, she marries seven brothers but never has a child. Then, she dies (Luke 20:27–32).

The Sadducees are trying to prove that the Mosaic law is incompatible with the resurrection of the dead. The assumption is that a woman can't be married to seven men. But this woman married seven, and after the resurrection they're all alive. So, whose wife is she?

Jesus points out that their scenario requires a false assumption: that there is marriage after the resurrection. There isn't (Luke 20:34–36). Once the woman dies, her marriages are fulfilled and resolved (Romans 7:2–3). This is not because they had no meaning, but because the purposes of marriage don't apply to the post-resurrection world.

Turning simple rebuttal into a devastating counter, Jesus then uses the Mosaic law and the Patriarchs to prove the resurrection is true (Luke 20:37–40).