Eruvin, Chapter 6, Mishnah 4. Our mishnah opens with a question of timing: from when may one renounce his rights? "Renouncing one's rights" (bittul reshus) is a declaration made by someone who did not join in the eruv, that his control of the courtyard - his share in the control of the courtyard - is null and void, so as to allow the other residents of the courtyard to carry from their houses into the courtyard. The question is at what time this may be done.
From when may one renounce his rights:
Beis Shammai: One must renounce his rights before Shabbos, while it is still day.
Beis Hillel: One may renounce even after dark, even after Shabbos has begun.
The Gemara explains that the root of the dispute lies in how we define the very nature of renouncing one's rights:
According to Beis Shammai: Renouncing one's rights is an act of transfer - the person conveys and hands over his control to the other residents, and a transaction of this sort is not within his power to perform on Shabbos.
According to Beis Hillel: This is not a transaction at all, but merely a withdrawal. The person declares that he will have no control in the courtyard, and as a matter of course, the control belongs to the others - not because he gave them anything, but because he removed himself.
One who renounced his rights and then took out his utensils:
The mishnah continues and discusses one who renounced his rights and afterward took his utensils out of his house into the courtyard before his fellow residents managed to take out their own utensils - an act that reveals their possession and control of the courtyard. What is the ruling regarding the one who took his utensils out?
Rabbi Meir (the anonymous first opinion of the mishnah): "bein b'shogeg bein b'meizid - harei zeh oser" - whether he took them out inadvertently, having forgotten and taken out his belongings, or whether he took them out deliberately in order to retract his renunciation, he forbids his neighbors to take things out from their houses into the courtyard, since he has nullified his renunciation of rights. It is worth noting that the essential reason applies to the deliberate case, but on account of the deliberate case we forbid even in the inadvertent case, in order to make the ruling uniform.
Rabbi Yehudah disagrees: "b'meizid oser, b'shogeg eino oser" - if he deliberately retracted his renunciation of rights before the others managed to take possession of the courtyard, he forbids them. But inadvertently he does not forbid them: since he took the utensils out unintentionally, this act does not reveal any retraction of his renunciation, and the other residents are permitted to take things out from their houses into the courtyard.
In summary: In this mishnah we learned the dispute between Beis Shammai and Beis Hillel about the time for renouncing one's rights - while it is still day or even after dark - which depends on the question of whether renouncing one's rights is a transfer or merely a withdrawal. We also learned the ruling concerning one who renounced his rights and then took out his utensils before his fellow residents took possession of the courtyard: according to Rabbi Meir he forbids them whether inadvertently or deliberately, and according to Rabbi Yehudah he forbids them only when he acted deliberately.