For the source text click/tap here: Beitzah 40
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The Mishnah on our daf teaches that a person who has guests come and visit on Yom Tov from the next city(i.e. they created an eruv techumim that allowed them to travel to him; he did not create such an eruv so neither he nor his possession can go to their city), cannot give them food to take back home with them, since the food belongs to him and is there for limited to areas that he is allowed to go to.
The convention of shlichut (halakhic agency) is a familiar and widespread concept in Halakha. Many halakhic activities such as kinyan, kiddushin, gittin, and hekdesh can be performed indirectly through an agent (shaliach).
As we leave our beloved Masechta let us look at the most erudite talmid of Prof Shaul Lieberman, Prof Dovid Weiss Halivni who revolutionized the way we look at Talmudic texts seeing the geological strata underneath the surface.