Genesis 18:9-13 meaning

They said to Abraham, "Where is Sarah your wife?" (v 9).Then Abraham is given advanced notice of Isaacs's future birth. The visitors will surely return to you at this time next year; and behold, Sarah your wife will have a son (v 10). In Genesis 15:4, Abraham was told that his heir would be a natural-born son. Then in Genesis 17:16-21, he was assured that Sarah would conceive the child. This time the promise is given with a specific timetable. The Lord said, about this time next year (Genesis 17:21; 2 Kings 4:16), Sarah will give birth to a son. 

Sarah was listening at the tent door (v 10). The tent door was likely a partition consisting of a cloth of woven goat hair creating rooms within a goat hair tent. So it would be easy for Sarah to listen to the proceedings. This verse provides the background for Sarah's reaction in verse 12. Abraham and Sarah were old, advanced in age…Sarah was past childbearing (v 11). Sarah had clung to the hope of having a child for many years. Then after being ten years in Canaan, Sarah finally concluded she was not going to have children and proposed that Abraham bear a child through her maid Hagar (Genesis 16:1-4). We are now fourteen years after the time Sarah had concluded she was barren. 

This shows that the conception and birth of Isaac were miraculous; it was biologically impossible. The beginning of the people of Israel was an extraordinary event. Perhaps this miraculous birth was a picture of the miraculous birth of Jesus. It seems fitting that the heir to the promise from whom all the nations of the earth would be blessed would be miraculously conceived. This also shows why Sarah laughed to herself (v 12). To Sarah it was hard to believe she could have a baby, so she laughed to herself." Although Sarah skeptically laughed, she was also a model of faith (Hebrews 11:11). 

Sarah asked, shall I have pleasure, my lord being old also? (v 12). The word "pleasure" is the Hebrew word 'ednah' and means sexual delight or the enjoyment of intimate love with one's spouse implying the ability to become pregnant. 

Now the Lord reveals He heard Sarah talking to herself saying, "why did Sarah laugh?" (v 13). Sarah's skepticism does not sidetrack, slow down, or stop the promise of God. She will still conceive, whether she thinks she can or cannot.