Our Mishna teaches that when a man dies, his children cannot insist that his widow move out of his house, even with a promise to support her. In fact, if she wants to remain, the orphans are obligated to give her a place in the house according to her needs (some say that she has full access to the house, as she did while her late husband was alive), and support her there.
In this context, our Gemara tells of various commands that Rabbi Yehuda HaNasi gave while on his deathbed. To his children his instructions were: “Take great care with regard to your mother’s honor, keep my candle burning and my table set, each in its proper place, and my servants, Josef Heifani and Shimon Efrati should serve me in my death as they did during my lifetime.” According to the Talmud Yerushalmi, Rabbi Yehuda HaNasi specifically instructed that his wife should remain in his home, which is a direct connection to our Mishna. Some suggest that he needed to emphasize this point because of the concern that there would be an argument about whether his house, as the home of the Nasi, perhaps had a unique status, and that his wife would not merit remaining in it.
The woman that Rabbi Yehuda HaNasi refers to as “your mother” was, in fact, a stepmother. Rav Ya’akov Emden points out that we already find in the Torah that a man may refer to his wife as his children’s mother, even if she did not give birth to them. When Ya’akov reacts to Yosef’s dream where the sun and the moon bow down to him (see Bereshit 37:10), he asks whether Yosef anticipates that his father, mother and brothers would all bow down – yet Yosef’s mother, Rachel, had already passed away. The Iyyun Ya’akov suggests that a woman who raised a child may be called his mother even if she is not his birth mother (see Rashi, ibid).