Gen 18:1 And the LORD appeared unto him in the plains of Mamre: and he sat in the tent door in the heat of the day;
Gen 18:2 And he lift up his eyes and looked, and, lo, three men stood by him: and when he saw them, he ran to meet them from the tent door, and bowed himself toward the ground,
Gen 18:3 And said, My Lord, if now I have found favour in thy sight, pass not away, I pray thee, from thy servant:
Gen 18:4 Let a little water, I pray you, be fetched, and wash your feet, and rest yourselves under the tree:
Gen 18:5 And I will fetch a morsel of bread, and comfort ye your hearts; after that ye shall pass on: for therefore are ye come to your servant. And they said, So do, as thou hast said.
Gen 18:6 And Abraham hastened into the tent unto Sarah, and said, Make ready quickly three measures of fine meal, knead it, and make cakes upon the hearth.
Gen 18:7 And Abraham ran unto the herd, and fetcht a calf tender and good, and gave it unto a young man; and he hasted to dress it.
Gen 18:8 And he took butter, and milk, and the calf which he had dressed, and set it before them; and he stood by them under the tree, and they did eat.
This episode begins in the hills of Hebron, and we see Abraham hanging out in the heat of the day. Most work would have been done at that time very early in the morning because by the middle of the day, probably in this instance, it was too hot to do anything. Abraham sees three men approaching and we are cast headlong into a strange thing…..” And the LORD appeared unto him in the plains of Mamre.”
The Lord or Adonai, is visiting Abraham. This word “Adonai” is a Hebrew word, and it translates to Lord or Master. The mystery here is that this is not the word used in the original Hebrew OT manuscripts. The actual word is “Yud-Heh-Vav-Heh” in the Hebrew alphabet, or YHWH in the English alphabet. This comes from a long standing Jewish tradition that in order to not use the Lord’s name in vain, you simply don’t say it, write it, or use it.
Early Jewish tradition tells us that these three men were angels:
THE VISIT OF THE ANGELS
The day whereon God visited him was exceedingly hot, for He had bored a hole in hell, so that its heat might reach as far as the earth, and no wayfarer venture abroad on the highways, and Abraham be left undisturbed in his pain. But the absence of strangers caused Abraham great vexation, and he sent his servant Eliezer forth to keep a lookout for travellers. When the servant returned from his fruitless search, Abraham himself, in spite of his illness and the scorching heat, prepared to go forth on the highway and see whether he would not succeed where failure had attended Eliezer, whom he did not wholly trust at any rate, bearing in mind the well-known saying, “No truth among slaves.” At this moment God appeared to him, surrounded by the angels. Quickly Abraham attempted to rise from his seat, but God checked every demonstration of respect, and when Abraham protested that it was unbecoming to sit in the presence of the Lord, God said, “As thou livest, thy descendants at the age of four and five will sit in days to come in the schools and in the synagogues while I reside therein.”
Meantime Abraham beheld three men. They were the angels Michael, Gabriel, and Raphael. They had assumed the form of human beings to fulfil his wish for guests toward whom to exercise hospitality. Each of them had been charged by God with a special mission, besides, to be executed on earth. Raphael was to heal the wound of Abraham, Michael was to bring Sarah the glad tidings that she would bear a son, and Gabriel was to deal destruction to Sodom and Gomorrah. Arrived at the tent of Abraham, the three angels noticed that he was occupied in nursing himself, and they withdrew. Abraham, however, hastened after them through another door of the tent, which had wide open entrances on all sides. He considered the duty of hospitality more important than the duty of receiving the Shekinah. Turning to God, he said, “O Lord, may it please Thee not to leave Thy servant while he provides for the entertainment of his guests.” Then he addressed himself to the stranger walking in the middle between the other two, whom by this token he considered the most distinguished,- it was the archangel Michael–and he bade him and his companions turn aside into his tent. The manner of his guests, who treated one another politely, made a good impression upon Abraham. He was assured that they were men of worth whom he was entertaining. But as they appeared outwardly like Arabs, and the people worshipped the dust of their feet, he bade them first wash their feet, that they might not defile his tent.
He did not depend upon his own judgment in reading the character of his guests. By his tent a tree was planted, which spread its branches out over all who believed in God, and afforded them shade. But if idolaters went under the tree, the branches turned upward, and cast no shade upon the ground. Whenever Abraham saw this sign, he would at once set about the task of converting the worshippers of the false gods. And as the tree made a distinction between the pious and the impious, so also between the clean and the unclean. Its shade was denied them as long as they refrained from taking the prescribed ritual bath in the spring that flowed out from its roots, the waters of which rose at once for those whose uncleanness was of a venial character and could be removed forthwith, while others had to wait seven days for the water to come up. Accordingly, Abraham bade the three men lean against the trunk of the tree. Thus he would soon learn their worth or their unworthiness.
Being of the truly pious, “who promise little, but perform much,” Abraham said only: “I will fetch a morsel of bread, and comfort ye your heart, seeing that ye chanced to pass my tent at dinner time. Then, after ye have given thanks to God, ye may pass on.” But when the meal was served to the guests, it was a royal banquet, exceeding Solomon’s at the time of his most splendid magnificence. Abraham himself ran unto the herd, to fetch cattle for meat. He slaughtered three calves, that he might be able to set a “tongue with mustard” before each of his guests. In order to accustom Ishmael to God-pleasing deeds, he had him dress the calves, and he bade Sarah bake the bread. But as he knew that women are apt to treat guests niggardly, he was explicit in his request to her. He said, “Make ready quickly three measures of meal, yea, fine meal.” As it happened, the bread was not brought to the table, because it had accidentally become unclean, and our father Abraham was accustomed to eat his daily bread only in a clean state. Abraham himself served his guests, and it appeared to him that the three men ate. But this was an illusion. In reality the angels did not eat, only Abraham, his three friends, Aner, Eshcol, and Mamre, and his son Ishmael partook of the banquet, and the portions set before the angels were devoured by a heavenly fire.
Although the angels remained angels even in their human disguise, nevertheless the personality of Abraham was so exalted that in his presence the archangels felt insignificant.
The Legends of the Jews, By Louis Ginzberg, 
It is Christian tradition that the visitors are two angels and an early incarnate visit from Jesus.
It is true that we call Jesus Lord, but if we look at the text in the proper view of the context then we can only conceive that this is referring to God Himself, but this leads to more questions than answers. On the one hand, we are told that no man can look upon God the Father and live. On the other, God is not limited to any laws in any and all universes and settings because frankly, He is God and He can do whatever He pleases.
This is complicated further by the fact that in verse two, the text says “men” or “enosh” which translates to physical, human, men and not spirit beings. These men also eat food that Abraham brings them; not something that spirit beings would normally do.
But by their discussions and actions in this chapter and the next, we know that these are more than men.
We will have to rely on the opinion that God is not limited to our understanding or doctrine, and that this is a strange physical appearance of God on the earth with two angels.