What does Mark 12:19 mean?

The Sadducees are asking a question about levirate marriages. In the ancient near-east, women were given in marriage to strengthen business ties or because her family of birth couldn't support her. Rarely did a man and woman marry because they were deeply in love with each other, or never wanted anyone else. Marriage was crucial for a woman's survival, as they usually had no right to own property and they would find it difficult to support themselves outside a family or clan. Like Naomi and Ruth, they needed a male relative who was willing to claim them. If their husband died and they had no son, their options were limited.

To protect young widows, the Mosaic law endorsed the levirate marriage (Deuteronomy 25:5–10). If a woman's husband died without a son, the husband's younger brother was obliged to marry the widow and provide a son in his name. The son would inherit the first husband's birthright and care for his mother.

This is what was supposed to happen with Tamar, Judah's daughter-in-law. When Judah's oldest son married Tamar but then died, his middle brother Onan was supposed to give Tamar a son. Onan refused; he knew that if Tamar had a son, the son would claim the firstborn birthright. If Tamar didn't have a son, Onan would become the firstborn. When Onan cheated Tamar, God killed him. Judah should then have given Tamar to his youngest son, but kept delaying in fear God would kill him, as well. Tamar finally took matters into her own hands and tricked Judah into sleeping with her. She gave birth to twin boys, one of whom is in Jesus' genealogy (Genesis 38).