He [Abraham] looked up and behold, three men were standing before him. He took note, he ran towards them from the entrance to the tent, and prostrated himself on the ground.
He looked up and behold, three men were standing: During the course of his conversation with G-d, Abraham was profoundly engrossed in the Divine revelation. Even during our own prayers, when we are the ones who initiate the Divine encounter, we are enjoined to first clear our minds of any distracting thoughts.
The fact that Abraham noticed the men, despite the intensity of his concentration, shows his extraordinary sensitivity to others.
This sensitivity is the key to hospitality. When offering hospitality to guests, a host must do much more than merely proffer a free meal. He must focus fully on his guests and their needs, display sincere concern for their welfare and comfort, take an interest in their conversation, and in general make them feel at home. Abraham was the paradigm of such sensitivity to others: in the very midst of a conversation with G-d, he took notice of three travelers and excused himself from G-d's presence to tend to their needs.