be'Elonei Mamre - in the groves of Mamre
The Torah informs us of the site where the circumcision took place. This was also the place where he received an immediate sign that G-d appreciated Avraham's deed.
We find that manifestations of G-d's Presence to the prophets occur by means of fire, wind, water and earth (either of the four basic raw material the terrestrial earth is made of).
G-d appeared to Moshe in a burning bush (Shemot 3:2). He also appeared to the entire Jewish nation in an environment of fire, "He let you see His great fire, and you heard His words out of the fire" (Devarim 4:36). In Shemot 24:17 G-d's manifestation is described as "a consuming fire on top of the mountain."
In connection with the ascent to heaven by the prophet Eliyahu we read in 2Melachim 2:1 "When Hashem was about to take Eliyahu up to heaven in a whirlwind..." In 1Melahcim 19:11 "There was a great and mighty wind; splitting mountains and shattering rocks by the power of Hashem."
We also encounter a manifestation of G-d through a mighty wind in Iyov 38:1 "The Hashem replied to Iyov out of the tempest and said..."
An instance of G-d manifesting Himself by means of water is found in Yechezkel 1:1 "It was in the thirtieth year... when I was in the community of exiles by the river Kevar..." We encounter another example of G-d manifesting Himself by means of water in Yechezkel 1:24 "I could hear the sound of their wings like the sound of mighty waters, like the sound of Shakai."
We find G-d manifesting Himself in connection with earth in Yechezkel 43:2 "the whole earth is filled with His glory." We also find a revelation described as "and the earth was lit up by His Presence."
In this instance, G-d manifested Himself to Avraham by means of a tree. The Midrash uses the word elonei mamre to emphasize the fact that these were trees ilanot. Actually, Mamre was the name of one of Avraham's close associates as we know form 14:13 "Mamre the Emori, the brother of Aner and Eshkol who were allies of Avram." Had the Torah only wanted to tell us that Avraham circumcised himself near the place where Mamre lived it would have been appropriate to describe the area as ar'vot mamre, the fields of Mamre. The emphasis on the word elonei shows that Torah wanted to draw our attention to the fact that we are talking about a tree or trees. When Avraham told the men who came to visit to rest "under one of the trees," this shows that there was more than one tree.
Why did G-d choose a tree to be the site at which He manifested Himself to Avraham on this occasion? It was because the angel was going to tell him that within a year he and Sarah would have a son. H would experience something similar to that which was experienced by an aged tree which still produced fruit.
It is written in Iyov 14:7-9 "There is hope for a tree; if it is cut down it will renew itself; its shoots will not cease. If its shoots are old in the earth, and its stump dies in the ground, at the scent of water it will bud and produce branches like a sapling."
We also have a verse comparing the righteous to trees in Tehillim 1:3 "He [the righteous] is like a tree planted beside streams of water which yields its fruit in season."