Our Gemara quotes a Mishna in Nedarim (90b) which teaches that originally if a woman made a statement that indicated that she could no longer live with her husband, the beit din would obligate him to divorce her and pay her ketuba. Later on, the Sages became concerned that a woman who no longer desired to be married to her husband would make one of these claims, so the ruling was changed.
The following statements are those that were deemed sufficient to end a marriage:
teme’a ani lekha – the wife of a kohen tells him that she had relations with another man, where even if it was a case of rape, he will have to divorce her
ha-shamayim beini le-veinkha – literally “the heavens separate us”
netula ani min ha-yehudim – the woman takes a vow never to engage in relations with any Jewish man.
The suggestions made by the Sages when they rescinded their original ruling were:
The woman will have to bring proof that she was raped
ya’asu derekh bakasha – literally “they should make entreaties”
The husband should use his powers to annul the vow, at least as it pertains to him (see Bamidbar ch. 30).
The second claim mentioned in the Gemara – ha-shamayim beini le-veinkha – as well as the response to it – ya’asu derekh bakasha – are left unclear in the Gemara, and are subject to different interpretations by the rishonim.
Rashi appears to follow the Talmud Yerushalmi, and explains that she is claiming that her husband chooses not to engage in sexual relations with her. In the words of the Yerushalmi, her argument is “just as the heavens are far from the earth, so my husband is far away from me.” According to the Babylonian Talmud (Nedarim 91a) her claim is that he is incapable of engaging in relations.
The suggestion that in order to resolve this claim ya’asu derekh bakasha is understood by Rabbeinu Tam to mean that they should engage in prayer (apparently he is working with the explanation that the husband is suffering from a disability that does not allow him to engage in relations). Rashi follows the explanation of the Yerushalmi and Rabbeinu Hananel who explain that a meal should be arranged where the couple will be encouraged to work out their issues. The rishonim point out that the intention is that neither should be forced into any action, rather the couple should be counseled to work out the differences that exist between them.