Genesis 18:6-8 meaning

The bread cakes were small round, thin, loaves of bread. The word "measures" is the Hebrew word seah. One "seah" equals approximately 11 quarts. So, 3 "measures" would be a little more than a bushel. This would yield much more bread than the three visitors, Sarah, and Abraham could possibly eat.

Abraham himself selects a tender and choice calf (v 7) for the main dish. The meat was costly and a rare treat, but Abraham did not hesitate to prepare a calf for his guest's meal. We see the expense which Abraham goes to in order to cater lavishly to his visitors.

He took curds and milk (v 8) which were side dishes to bring out the taste of the meat and to quench the visitor's thirst. The word "curds" is the Hebrew word hemah which refers to curdled milk that is much like yogurt. In fact, it is made by churning milk just like making butter (cf. 2 Samuel 17:29; Proverbs 30:33). It was a staple of the diet of the Israelites, they even ate it from infancy (cf. Deuteronomy 32:14; Isaiah 7:15, 22). Milk was highly esteemed in the ancient world and regarded as a source of vitality. 

He was standing by them…as they ate (v 8). A mark of the highest courtesy, Abraham (the head of the household) stood (like a servant) while his guests ate. Here and in Genesis 19:3 we see heavenly beings (Angels, including the Lord) eating earthly food. Although they were not human, they appeared in a form that could perform physical acts as a human being would (Genesis 19:10, 32:24, 30; Hosea 12:3-4). Eating together was important in making or confirming covenants (Exodus 24:9-11; Matthew 26:17-30; Acts 2:42; 1 Corinthians 11:20-34). Therefore, when God was ready to expand the covenant promise to Sarah, he came in person to share a meal with Abraham.