This Mishnah addresses a fundamental question in the laws of eruvin: a person who has rights to a house in the courtyard but is not present there on Shabbos - does he create the prohibition and the need to join in the eruv, or does his absence remove his dwelling from the calculation altogether?
The wording of the Mishnah: "HaManiach es beiso v'halach lishbos b'ir acheres, echad nochri v'echad Yisrael - harei zeh oser, divrei Rabbi Meir" - one who leaves his house and goes to spend Shabbos in another city, whether he is a non-Jew or a Jew, restricts the others; these are the words of Rabbi Meir. In other words, even though he is not present in his house in the courtyard, this does not nullify his dwelling: if he is a Jew, he must join in the eruv, and if he is a non-Jew, the residents of the courtyard must rent his share from him.
The views of the Tannaim in the Mishnah:
Rabbi Meir: whether a non-Jew or a Jew - "harei zeh oser" - he restricts the others. His reasoning is that he holds the principle of "dirah b'lo ba'alim" - a dwelling without owners: a place fit for dwelling that currently has no owner or renter present is still considered a full dwelling, as though he were living there, and therefore one must either join him in the eruv or rent from him.
Rabbi Yehudah: "eino oser" - he does not restrict the others. As long as the person is not present in the place, his dwelling creates no prohibition.
Rabbi Yosi: "nochri oser v'Yisrael eino oser" - a non-Jew restricts but a Jew does not, and his reasoning is "she'ein derech Yisrael lavo b'Shabbos" - it is not the way of a Jew to return home on Shabbos; once he has left, he has left. A non-Jew, however, may well return on Shabbos. It emerges that fundamentally Rabbi Yosi holds like Rabbi Yehudah, that a dwelling without owners does not restrict, and that someone who does not actually live there creates no prohibition. The difference between them is this: Rabbi Yosi emphasizes that the non-Jew restricts precisely because he may arrive on Shabbos, whereas the Jew will not arrive.
Rabbi Shimon: "Afilu hiniach beiso v'halach lishbos etzel bito b'osah ir - eino oser, shekvar hisia mi'libo" - even if he left his house and went to spend Shabbos at his daughter's home in that same city, he does not restrict, since he has already put it out of his mind. Rabbi Shimon is speaking of a Jew who remained within the city and left his house to go to his daughter: even though technically he could return, we are not concerned about that, since he has already removed from his mind any thought of dwelling in his own house for this Shabbos. Once he has gone to spend Shabbos there, we do not suspect that he will change his mind and leave.
The Gemara's precision: why specifically at his daughter's home?
The Gemara adds an interesting qualification here: the Mishnah's ruling was stated specifically about one who goes to spend Shabbos at his daughter's home. The Gemara points to a social reality - at his daughter's home there is no concern that he will get into a quarrel with his son-in-law, and therefore he will certainly remain there for Shabbos. But regarding one who goes to spend Shabbos at his son's home, there is no complete assurance that he will remain, since we are concerned that friction may arise with his daughter-in-law and he will be forced to return home on Shabbos. This, then, is why the Mishnah used the word "his daughter" and not "his son."
In summary: in this Mishnah the Tannaim disagree about the status of an absent resident. According to Rabbi Meir, based on the principle of "a dwelling without owners," both the non-Jew and the Jew restrict; according to Rabbi Yehudah, an absent resident does not restrict at all; according to Rabbi Yosi, the non-Jew restricts because it is his way to come on Shabbos, while the Jew does not restrict; and according to Rabbi Shimon, even one who goes to spend Shabbos at his daughter's home in the same city does not restrict, since he has already put his own house out of his mind. The Gemara explains that this was stated specifically about his daughter's home and not his son's, because of the concern that he may be forced to return.