Before us is Mishnah 3, which deals with a widow's right to continue living in her late husband's house after his death. As we learned at the beginning of the chapter, the widow is supported from the assets of the estate; here the Mishnah comes to clarify where she is supported, and what claims the heirs may raise against her.
The widow who wishes to remain in her husband's house:
The widow turns to the heirs of the estate and says: "eini rotzah lazuz mibeis ba'ali" - she wishes to go on living in her late husband's house. In this case the Mishnah rules: "ein hayorshin yecholin lomar lah 'lechi leveis avich va'anan zaninan otach'" - the heirs cannot tell her to leave the house and return to her father's house, and that they will support her there as is their obligation. Rather, "zanin otah beveis ba'alah" - their obligation is to support her specifically in her husband's house.
And not only that, but "venosnin lah medor lefi kevodah" - they must place at her disposal living quarters within the house that befit her dignity.
The Gemara brings a beraisa that expands her rights, including within them:
The household servants - she is entitled to make use of them.
Bedding and utensils - she has the right to use these as well.
The rule is that just as she conducted herself during her husband's lifetime, so she may conduct herself after his death. All of these are part of the conditions of the kesubah that her husband obligated himself to her.
The widow who wishes to return to her father's house:
And what is the law when she says the opposite? "eini rotzah lazuz mibeis abba" - that is, she asks to remain in her father's house and not to live in her husband's house. In this case, "yecholin hayorshin lomar lah: 'im at etzleinu - yesh lach mezonos, ve'im ein at etzleinu - ein lach mezonos'". That is, if she stays with them in her husband's house, they will provide her with her support; but if she chooses to return to her father's house, they are not obligated in her support.
The Gemara explains the reason for this: "birkas habayis merubah" - blessing rests upon a house that has many people in it. There is a kind of economy of scale here, and the members of the household also help one another and benefit from one another. As long as she remains within the house, there is a benefit to her living there; but if she intends to leave the house, and we are left with nothing but to support her from the outside - to that the heirs are not obligated.
The claim of "she is young and they are young":
However, if the widow claimed that she is a young woman and the heirs are also young, and it is not proper for her to stay with them in the same house (and these are not her own children, for she is his second wife) - she has a justified claim for not remaining in her husband's house, and therefore "zanin otah vehi beveis avihah", and the heirs are obligated to support her even though she is living in her father's house and not in her husband's house.
In summary: In this Mishnah we learned that a widow who chooses to remain in her husband's house is entitled to support there, to living quarters befitting her dignity, and to the use of the servants, the bedding and the utensils just as she was accustomed during her husband's lifetime, and the heirs cannot send her off to her father's house. By contrast, one who chooses on her own initiative to live in her father's house - the heirs may withhold support from her, on the grounds of "birkas habayis merubah". But when she has a justified claim, such as the claim of "she is young and they are young", they support her even in her father's house.