From the Rebbe’s explanation:
The first verse of Vayeira describes a unique divine revelation experienced by Avraham. However, in the middle of this revelation Avraham excuses himself from G‑d’s presence to rush toward three wayfarers and offer them hospitality.
G‑d appeared to Avraham…but he looked up and saw that there were three men… (Breishit 18:2)
The three men that Avraham greeted and invited into his home turned out to be malachim (“angels”) – messengers from Above. Malachim don’t need food or water. They do not need a shelter from the sun or a place to sleep. As Rashi points out in his commentary, they only pretended to eat and drink out of respect for Avraham.
If so, what did Avraham accomplish? He served food and drinks to someone who did not need it! Was it worth it to walk out from his audience with haShem for this purpose? And moreover, why do we learn the greatness of Avraham’s hospitality from this example?
Avraham put aside his encounter with G‑d in order to greet his guests. From this we learn that hosting guests is so great that it takes priority over an encounter with G‑d. (Rambam, Mishneh Torah)
Yet indeed we learn more from this episode than from any other. It shows that the main secret of hospitality is not the food, not the drinks and not the comfortable bed. The crucial ingredient of hosting guests is to show them that you care. This is something that Avraham and Sarah exemplified to perfection.
Based on the Rebbe’s talk (Likutei Sichot vol. 25, p. 78).