According to Augustine, it seems, he interpreted the three men in Genesis 18 as The Trinity God appearing in human form, hence the three men.
On the Trinity (Book II) - Chapter 10
But under the oak at Mamre he saw three men, whom he invited, and
hospitably received, and ministered to them as they feasted. Yet
Scripture at the beginning of that narrative does not say, three men appeared to him, but, "The Lord appeared to him." And then, setting
forth in due order after what manner the Lord appeared to him, it has
added the account of the three men, whom Abraham invites to his
hospitality in the plural number, and afterwards speaks to them in the
singular number as one; and as one He promises him a son by Sara, viz.
the one whom the Scripture calls Lord, as in the beginning of the same
narrative, "The Lord," it says, "appeared to Abraham." He invites them
then, and washes their feet, and leads them forth at their departure,
as though they were men; but he speaks as with the Lord God, whether
when a son is promised to him, or when the destruction is shown to him
that was impending over Sodom.
Genesis 18 is taken seriously by many Trinitarians to prove that Trinity is mentioned in the Old Testament. The language used in Genesis 18 is vague and subjected to many interpretations. This has to be one of the most debated passages of all time. Non-Trinitarians and even some Trinitarians understand this as "God and two angels". However, as a Trinitarian, I prefer to believe that it was The Trinity who visited Abraham.
Explanation why the two men were not merely angels
Genesis 19 called the two men as angels. However, as the language here is vague, it seems the two angels were also the Lord(or Lords). For they said "we are going to destroy this place" and then later the Bible says "God destroyed the cities".
(Genesis 19, NIV)
(1) The two angels arrived at Sodom in the evening, and Lot was sitting in
the gateway of the city. When he saw them, he got up to meet them and
bowed down with his face to the ground.
(12) The two men said to Lot, “Do you have anyone else here—sons-in-law,
sons or daughters, or anyone else in the city who belongs to you? Get
them out of here, (13) because we are going to destroy this place.
The outcry to the Lord against its people is so great that he has sent
us to destroy it.”
(24) Then the Lord rained down burning sulfur on Sodom and
Gomorrah—from the Lord out of the heavens.
(29) So when God destroyed the cities of the plain, he remembered
Abraham, and he brought Lot out of the catastrophe that overthrew the
cities where Lot had lived.