The Mishnah discusses a man who marries a woman, and at the time of the marriage she stipulated with him that he support her daughter from another marriage for five years. The halachah is that he is obligated to support the daughter for those five years, in accordance with the agreement he made.
The obligation of the second husband:
The Mishnah adds: if the woman later married another man, and she stipulated with him as well that he support that same daughter for five years, he too is obligated to support her for five years. The first husband's obligation is not dependent on the marriage remaining intact, since the agreement was made separately from it; therefore he is obligated to support her whether they remained married or were divorced, and the second husband is bound by the agreement he made on his part.
The claim of "Likhshetavo Etzli":
One might argue that the daughter has no need for support from two stepfathers - one a former stepfather and the other a present one. Regarding this the Mishnah rules that the first husband cannot say that he will support her only when she comes to him. This claim could carry two possible meanings:
That she come to his home and actually be supported there.
That had the marriage to her mother continued, he would have supported her under those circumstances.
Rather, he must bring her food to the place where her mother is living, or send her money. The obligation rests upon him in any case, and that is the Mishnah's point.
"Echad Zan V'Echad Nosein D'mei Mezonos":
The Mishnah further rules that the two husbands cannot jointly say: "We will support her together and split the cost between us." Rather, one gives her actual food, and the other gives her the monetary value of the food. The reason is that the obligation is purely financial, and it is not based on the daughter's needs, but on an obligation to give a certain sum corresponding to the standard quantity of food. For this reason the obligation cannot be divided between the two men, since the matter does not concern what the daughter receives, but what each one of them obligated himself to give.
In summary: We learned that one who obligates himself at the time of marriage to support his wife's daughter for five years is bound by that commitment, and his obligation stands on its own and is not dependent on the continuation of the marriage. Therefore, when the mother married another man and stipulated a similar condition with him, both are obligated: the first cannot make her support conditional upon her coming to him, but rather he brings her food to her mother's place; and the two of them do not support her together, but rather one provides food and the other gives the monetary value of the food - since the commitment is a financial obligation of each one of them, and not a response to the daughter's needs.