Gen. 18:1 (ESV) And the LORD appeared to him by the oaks of Mamre, as he sat at the door of his tent in the heat of the day.
Abraham sits at the opening of his tent to receive the channeled breeze through the doorway. This would have been the place where he received and entertained guests – the first room in the tent.
Gen. 18:2-5 (ESV) He lifted up his eyes and looked, and behold, three men were standing in front of him. When he saw them, he ran from the tent door to meet them and bowed himself to the earth and said, “O Lord, if I have found favor in your sight, do not pass by your servant. Let a little water be brought, and wash your feet, and rest yourselves under the tree, while I bring a morsel of bread, that you may refresh yourselves, and after that you may pass on—since you have come to your servant.” So they said, “Do as you have said.”
Abraham runs in order to show his eagerness to care for the travelers. In bowing himself to them he is showing that he is physically willing to serve them and care for them (cf. Gen 19:1). He also makes it clear that he is not their superior despite his obvious wealth that the three men would have seen while being within the midst of his camp (Gen. 13 describes the wealth of Abraham). This may show that the hospitality of the ancient near east in relation to hosts and strangers transcended rich and poor realities.
Abraham plays the role of ancient near eastern host perfectly by further defining his relationship to them, calling them master and himself their servant. He then makes his offer to the road-weary travelers – water, washed feet, rest, and food – with the understanding that “after (the refreshments) you may pass on.” It is difficult to tell if Abraham is intending for them to leave after his hospitality, only expecting them to press on, or a combination of the two. The travelers accept Abraham offer (maybe after an initial refusal Moses probably is not giving us every detail in this interchange) and they are temporarily brought into Abraham’s protection and care, into his beit av.
Gen. 18:6-8 (ESV) And Abraham went quickly into the tent to Sarah and said, “Quick! Three seahs of fine flour! Knead it, and make cakes.” And Abraham ran to the herd and took a calf, tender and good, and gave it to a young man, who prepared it quickly. Then he took curds and milk and the calf that he had prepared, and set it before them. And he stood by them under the tree while they ate.
Abraham snaps into action. He starts the process of preparing a three-course meal of the best of his wealth. The first step is to go into the tent of Sarah – to go to her domain and have her spring into her role as food preparer. This would serve as the appetizer to the guests. Abraham then goes and finds a calf suitable for his guests, "tender and good," the equivalent of prime – for Abraham choice or select simply would not do. The loss of a calf was a huge financial blow for Abraham, cattle were generally uncommon for semi-nomads like Abraham and the death of one at a young age cost him future dairy products and calves. His decision to slaughter the calf is a testament to his sizable wealth and devotion to being a good host to his special guests. Next he delegates the household cook to barbeque the calf while he collects the milk and curds (which were/are a delicacy). Abraham now has all three elements of the meal going at the same time, maximizing his efficiency in order to serve his guests. After the meal is finished Abraham himself serves his guests. Interestingly the text says that he “stood by while they ate” Abraham does not even take part in the meal that took over half a day to make.
Gen. 18:9 (ESV) They said to him, “Where is Sarah your wife?” And he said, “She is in the tent.”
Once again Abraham’s role is seen as presenter and host by the absence of his wife. The fact that the guest even asks about Sarah is odd, because he would have obviously understood that she was in her place in her tent. The question is meant to sound odd and draw emphasis to the fact that the speaker is someone of importance with an important message to deliver.
Gen. 18:10-15 (ESV) The LORD said, “I will surely return to you about this time next year, and Sarah your wife shall have a son.” And Sarah was listening at the tent door behind him. Now Abraham and Sarah were old, advanced in years. The way of women had ceased to be with Sarah. So Sarah laughed to herself, saying, “After I am worn out, and my lord is old, shall I have pleasure?” The LORD said to Abraham, “Why did Sarah laugh and say, ‘Shall I indeed bear a child, now that I am old?’ Is anything too hard for the LORD? At the appointed time I will return to you, about this time next year, and Sarah shall have a son.” But Sarah denied it, saying, “I did not laugh,” for she was afraid. He said, “No, but you did laugh.”
Once again Sarah is shown behind the scene, “listening at the tent door” unseen and trying to remain unnoticed. Moses provides an epexegetical statement to explain the heir/inheritance situation with Abraham and Sarah. For Sarah the fact that she has not provided Abraham with an heir has been a constant weight of shame upon her, since family and land are the most important possessions one can have and she is the chosen wife of inheritance. If she does not bear a son then the line of Abraham dies and the promises of God have failed. Despite that it seems that Sarah has come to grips with the fact that she will never bear Abraham children since she was already well past menopause. When Sarah denies laughing she might be trying to not offend the guest.