Genesis 18:1

וירא אליו. [Hashem] appeared to him. To visit the sick (Sotah 14a, Tanchuma Yashan 1). The amora R' Chama the son of Chanina said: It was the third day since his circumcision, and the Holy One, Blessed is He, came and inquired about [Abraham's] welfare.

AND the glory of the Lord was revealed to him in the valley of Mamre; and he, being ill from the pain of circumcision, sat at the door of the tabernacle in the fervour (or strength) of the day.

AND HE APPEARED TO HIM. Rashi comments: “To visit the sick man. Said Rabbi Chama the son of Chanina, ‘It was the third day after his circumcision, and the Holy One, blessed be He, came and inquired after him.’ And, lo, three men: angels who came to him in the form of men. Three: one to announce to Sarah that she would bear a son, one to heal Abraham, and one to overthrow Sodom. Raphael who healed Abraham went from there to rescue Lot” for these do not constitute two commissions. This is because the second mission was in another place, and he was commanded thereon after [he had completed his first mission]. Perhaps it is because the two missions had rescue as their common goal. “And they did eat: they appeared to be eating.”
In the book Moreh Nebuchim it is said that this portion of Scripture consists of a general statement followed by a detailed description. Thus Scripture first says that the Eternal appeared to Abraham in the form of prophetic visions, and then explains in what manner this vision took place, namely, that he [Abraham] lifted up his eyes in the vision, and lo, three men stood by him, and he said, if now I have found favor in thy eyes. This is the account of what he said in the prophetic vision to one of them, namely, their chief.
Now if in the vision there appeared to Abraham only men partaking of food, how then does Scripture say, And the Eternal appeared to him, as G-d did not appear to him in vision or in thought?, when in the detailed account of the vision it is explained that he saw only angels? Such is not found with respect to all the prophecies. And according to his words, Sarah did not knead cakes, nor did Abraham prepare a bullock, and also, Sarah did not laugh. It was all a vision! If so, this dream came through a multitude of business, like dreams of falsehood, for what is the purpose of showing him all this! Similarly did the author of the Moreh Nebuchim say in the case of the verse, And a man wrestled with him, that it was all a prophetic vision. But if this be the case, I do not know why Jacob limped on his thigh when he awoke! And why did Jacob say, For I have seen an angel face to face, and my life is preserved?, Verse 31. The prophets did not fear that they might die on account of having experienced prophetic visions. Jacob, moreover, had already seen a greater and more distinguished vision than this since many times, in prophetic visions, he had …

'וירא אליו ה. In what manner did G’d appear to Avraham here? Three men, who turned out to be angels came to him. There are numerous examples in Scripture where the angels or a single angel are described as “G’d”, i.e. seeing they are G’d’s agents they are described as ה', even though what is meant is an agent, an angel. To mention just one or two such examples: Exodus 23,21 כי שמי בקרבו, “because My Holy Name is within him.” Or, Exodus 3 3,2 וירא אליו מלאך ה' בלבת אש מתוך הסנה, “an angel of Hashem appeared to him in the form of a flame of fire in the midst of the thorn bush.” [the unusual fire which failed to consume, destroy, the thorn bush represented a Divine appearance. Ed.] Or, in verse 4 of the same chapter: וירא ה' כי סר לראות, “when G’d (i.e. the angel) saw that he had turned aside to watch the spectacle.”

כחום היום, why would the Torah need to relate this apparently inconsequential piece of information (so that we read it aloud every week after over 3000 years)? The point the Torah wanted to make was that in the event that we compare Lot’s reception of the angels, when he offered them lodging for the night, (Genesis 19,1) whereas Avraham only offered light refreshment, the reason for this is that the angels came to Lot in the evening, a time for travelers to find lodging, whereas here, seeing that they arrived during the midday heat, there was no reason to assume that they would not want to continue their journey.

וירא אליו ה' באלוני ממרא, because this was where Avraham had circumcised himself at that time. His whole household had been circumcised with him at the time. This is where G’d manifested Himself as a sign that He stood by the covenant, similar to the verse at the beginning of Deuteronomy 29,9-11, commencing with the words אתם נצבים היום, and to Kings II 23,3 ויכרות לפני ה'. He appeared to Avraham seeing he was the individual most deserving to be the recipient of such a vision. We have a similar occurrence in Exodus 4,24 ויפגשהו ה', where G’d “met” with Moses without delivering an oral message. At that time G’d’s purpose was to ensure that Moses would circumcise his son, to maintain the covenant which was to be an eternal covenant with the descendants of Avraham as spelled out in Genesis 17,11-12. Perhaps this is the reason why a chair is prepared at the occasion of the circumcision (Pirkey de Rabbi Eliezer 29, as well as Zohar Bereshit 13,10) This chair alludes to the fact that hopefully, the presence of G’d will attend this marking of the sign of the covenant by a new member of the Jewish people.

וירא ה' אליו באלוני ממרא, in the location where Avraham dwelled, as we know from Genesis 14,13 והוא שוכן באלוני ממרא האמורי, “he dwelled by the groves of Mamre the Emorite. The reason why Avraham had not moved away from there was that his allies also lived in that proximity. Solomon advised already in Proverbs 27,10:טוב שכן קרוב מאח רחוק, “better a good neighbour who lives close by than a brother who lives far away.” G’d appeared to him there after he kept the commandment to circumcise himself, in order to apprise him of what he had in store for Sodom, a city in which his nephew had made his home. Avraham was the outstanding human being in that generation. Seeing that G’d was bent to exact partial retribution for the worst outrages committed by mankind at that time, He did not want to do so before informing Avraham of His intention. It was G’d’s intention to demonstrate that He does keep track of what individuals in the “lower” part of His universe are up to, and that He even will not exact collective punishment unless He can demonstrate that the parties affected are all guilty. There was no need for G’d to “descend” to investigate what He already knew, but the Torah describes this in terms that we can understand. He wanted to enable Avraham when the latter would instruct and teach his descendants to walk in the ways of G’d, to show that His ways were truly not only just but that He made allowances for human weaknesses. It is possible, -if this was indeed G’d’s purpose- to explain the entire paragraph as a prophetic vision up until verse 23 where the Torah writes that Avraham returned to his station, i.e. that this line terminated the prophetic vision יושב פתח האהל, as explained immediately following,

וירא אליו ה' באלוני ממרא, “The Lord appeared to him at eloney mamre, etc.” According to Rashi, Mamre was the man who had advised Avraham strongly to carry out G–d’s command to circumcise himself. This is why this revelation took place while Avraham was on his property. The obvious question here is why someone of the stature of Avraham needed to consult with his friends about if and how to relate to G–d’s commandment. He had been tested as to his faith in Him on ten occasions, and he had passed all these tests without consulting with anyone, why would he suddenly feel the need to “consult” anyone? The answer clearly must be that Avraham did not “consult” with anyone in order to decide if to carry out G–d’s command; he only asked his friends if to perform this commandment on himself in the privacy of his tent or publicly, in order to demonstrate his loyalty to G–d’s command. His purpose in doing so publicly would be in order to encourage others to emulate his example. When the Torah described him as performing the act of circumcision בעצם היום הזה, (Genesis 17,23) these words mean: “in broad daylight, for all to see.” Mamre was given credit by G–d for having given Avraham this advice. A different interpretation of our verse: Avraham consulted with Mamre regarding the exact part of his body where the “circumcision” had to be performed. He therefore advised him to perform this operation on the organ that represented his masculinity. After all, G–d had restricted the performance of this rite to the males of the species. (17,10) He also advised him to commence with circumcising himself and his son Ishmael first. Once his slaves and friends would observe this, most of them would follow willingly without protest. The Torah testifies in chapter 17, verse 27 that all the members of Avraham’s household (including hired help) were circumcised on the same day that he was. If you were to ask why Mamre, himself, who gave Avraham this advice, did not have himself circumcised also, the answer is that eventually he did do so as reported in a Midrash.

כחם היום, “during the hottest part of the day.” This is the time at which people consume their lunch. This was usually during the fourth hour of the day. This is in accordance with the commentary of Rav Papa in the Talmud, tractate Shabbat folio 10. Avraham at the time was on the lookout for prospective guests at the entrance to his tent.