The Lord's visit to Abraham set the time for Isaac's birth. The three visitors were probably the Lord and two angels (see study note on 16:7). Abraham welcomed the visitors peacefully and generously, which contrasted with the chaos and corruption in Sodom (chapter 19).
Sharing a meal was important for making or confirming covenants. When God was ready to fulfill the covenant promise, he personally shared a meal with Abraham. Fellowship with God has always included a communal meal (see Exodus 24:9–11; Matthew 26:17–30 // Luke 22:7–38; Acts 2:42; 1 Corinthians 11:20–34).