Genesis 18:2

And he lifted up his eyes and looked, and, behold, three angels in the resemblance of men were standing before him; (angels) who had been sent from the necessity of three things;--because it is not possible for a ministering angel to be sent for more than one purpose at a time;--one, then, had come to make known to him that Sarah should bear a man-child; one had come to deliver Lot; and one to overthrow Sedom and Amorah. And when he saw them, he ran to meet them from the door of the tent, and bowed himself on the earth.

STOOD OVER HIM. The purport thereof is that they were standing opposite Abraham and looking at him, the expression being similar to: that stood over the reapers; the chief officers that stood over the work. And due to the fact that he [Abraham] was sitting and they were standing and looking at him, the verse says, “over him.” This is also the meaning of the expression, And he saw, and ran to meet them, for as he saw them standing opposite him and not continuing their journey, he ran to meet them in order to bring them to his house.
The sense of the expression, From the tent door, is that Abraham was still sitting there after the vision of the Shechinah had departed from him.
It is possible that the expression “over him” refers to the tent, i.e., that they were near it on the side which was not opposite the door, and there they stood and did not approach Abraham, just as in the verse, encamping ‘al’ (on) the sea. means “standing alongside him.”

וישא עיניו, he concentrated on seeing more clearly.

נצבים עלי, facing him. They appeared as if waiting to speak to him when he would be free to turn his attention from the marvelous manifestation he had just observed. People waiting to speak to someone are described as נצבים עליו, as for instance in Genesis 45,1 להתאפק לכל הנצבים עליו.

וירץ לקראתם, before they could open a dialogue with him.

מפתח האהל, he began running from the entrance of his tent. When a person is observed to perform any task with speed, with keenness, this reflects that he considers what he is about to do as important. We have another example of such conduct in Exodus 34,8 וימהר משה ויקוד ארצה וישתחו, “Moses hastened to bow down and to prostrate himself.”

וישתחו ארצה, seeing that the appearance of these strangers was so awe-inspiring. We have a parallel verse in Judges 13,6 when Manoach’s wife is described as reacting to the angel’s awe-inspiring appearance as such that she did not even dare to enquire his name, etc. Avraham considered these men as emissaries from some king.

וישא את עיניו, the first thing Avraham saw after he had gone to sleep were three men standing next to him, נצבים עליו, apparently ready to be of service to him. The meaning of the expression נצבים עליו is similar to Samuel I 22,7 ויאמר שאול לעבדיו הנצבים עליו, “Saul said to the people standing next to him (in attendance) etc.” The same expression is also used in this context in Ruth 2,6 הנצב על הקוצרים, “who was standing next to the reapers;” we also find this expression in Kings I 5,30 "משרי הנצבים, and in numerous other places in Scripture. These three men beheld by Avraham were standing at his disposal. They did not move, but indicated that they were expecting instructions from him. When he realised this he ran toward them. This explains why the word וירא, “he saw” appears twice in this verse in close succession.

מפתח האהל, where he had been sitting. He saw himself running towards these men in his vision.

וישתחו ארצה, they appeared to him to be men of great stature. He then addressed them with the words reported in the Torah. Our sages (Bereshit Rabbah 50,2) say that Avraham was so familiar with the sight of angels that their sudden appearance did not cause him to become disoriented, frightened and he perceived them essentially as אנשים, men. On the other hand, Lot, whose spiritual powers were quite minor, perceived the men as being angels, מלאכים, seeing that he had had little experience with such phenomena. (compare 19,1) Manoach’s wife had already told her husband that the face of the man who had told her that she would have a son was like that of an angel of G’d. (Judges 13,6)