What does Genesis 18:12 mean?

Abraham is speaking with three strangers who appeared near his tent. His first response to their arrival was to prepare a large, sumptuous feast of bread and meat. As Abraham will now know for sure, these men are actually a physical manifestation of God and two angels. Standing in the nearby tent, Sarah has heard the Lord's statement that by this time next year she would have a son. It's unclear whether or not Sarah understood at this point that it was the Lord speaking.

What Sarah did understand is that she had been barren her entire life, unable to conceive a child with Abraham. Now at the age of 90 or so, she had passed menopause. Some commentators suggest that she and Abraham, about 100 himself, had long since stopped even having intercourse.

All of the evidence of Sarah's life told her that having a baby was impossible. So, her initial response to the idea was the same as Abraham's had been: Sarah laughed in unbelief. That response seems entirely understandable to us. The Lord, however, will gently rebuke her for it in the following verses. That rebuke, in a humorously ironic way, will include the name of the child she is about to conceive: Isaac, meaning "he laughs."