In some situations, Birkat Ha’mazon is required by Torah law, and in other situations, it is required Mi’de’rabbanan – by force of Rabbinic enactment. The practical difference between a Torah obligation and one required Mi’de’rabbanan is in cases of Safeik – uncertainty. If one ate and cannot remember whether or not he recited Birkat Ha’mazon, then if the situation is such that Birkat Ha’mazon was required on the level of Torah law, then he must recite the first three blessings of Birkat Ha’mazon. In cases of uncertainty involving Torah law, we must be stringent, and so when there is uncertainty in a case where Birkat Ha’mazon was required by the Torah, one must recite the first three blessings (as the Torah obligation includes only the first three blessings). If Birkat Ha’mazon was required "Mi’de’rabbanan," then one can be lenient in situations of uncertainty, and so he does not recite Birkat Ha’mazon.
The basic rule is that the Torah obligation applies if a person ate at least a Ke’zayit of bread and he experiences "Sebi’a" – satiation. The Torah introduces the command of Birkat Ha’mazon by stating, "You shall eat and you shall be satiated, and you shall bless Hashem your G-d," and so the obligation depends on the experience of satiation. Therefore, even if one ate a large quantity of food, if he does not feel satiated, Birkat Ha’mazon is required only "Mi’de’rabbanan." Conversely, if one ate only a "Ke’zayit" of bread and feels satiated, then he is obligated to recite Birkat Ha’mazon on the level of Torah law.
It must be noted that one does not have to receive satiation only from bread for the Torah obligation to apply. Even if the satiation came from the combination of bread and other foods, the Torah obligation applies.
According to some Rishonim, the Torah obligation applies only if a person is "satiated" in regard to both hunger and thirst. This means that even if a person ate to the point of satiation, the Torah obligation of Birkat Ha’mazon does not apply if he feels thirsty. According to this opinion, the obligation applies in such a case only "Mi’de’rabbanan" unless the individual drinks and quenches his thirst.
This is the view accepted by the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909), in Parashat Hukat (Shana Rishona). He writes that if a person is "Ta’eb Li’shtot" – meaning, he feels a need to drink – he is not considered "satiated" and thus the Torah obligation of Birkat Ha’mazon does not apply. This does not mean that one must always drink during a meal for the Torah obligation to apply; it means that the Torah obligation does not apply if a person feels thirsty. If a person did not drink and does not feel thirsty, then the Torah obligation applies even according to this opinion.
Most other Rishonim, however, disagree, and maintain that thirst is not a factor with regard to the Torah obligation of Birkat Ha’mazon, and one who ate to the point of satiation is required to recite Birkat Ha’mazon on the level of Torah law even if he is thirsty.
In light of this difference of opinion, if one feels thirsty after eating, it is preferable to drink and quench his thirst so that he will have the opportunity to fulfill the Torah obligation of Birkat Ha’mazon according to all opinions.
Summary: The Torah obligation of Birkat Ha’mazon applies if one ate at least a Ke’zayit of bread, and he ate to the point of satiation (even if his satiation resulted from the combination of bread and other foods). If one ate a Ke’zayit or more and does not feel satiated, he is required to recite Birkat Ha’mazon only on the level of Rabbinic enactment. This difference is practically relevant in a case where one does not remember if he recited Birkat Ha’mazon – in such a case, if Birkat Ha’mazon is required as a Torah obligation, the person must recite the first three blessings of Birkat Ha’mazon, but if it is required by the Rabbis, he does not. According to some opinions, the Torah obligation does not apply if a person is thirsty, and so it is preferable for a person who feels thirsty after eating a meal to drink and quench his thirst so he can fulfill a Biblical Misva according to all opinions.
