In Bentching (grace after meals) - both in the Ashkenazic and in the Sefardic version - we say V'Al Brischa SheChasamta Bivsoreinu - ועל בריתך שחתמת בבשרנו - "and for Your covenant, which you sealed on our flesh". This refers, presumably, to the Brit Mila. Does a lady say these words? Why?
The Mishna Berura says:
בימינו נהגו הנשים לומר ג"כ על בריתך שחתמת בבשרנו ועל תורתך שלמדתנו וכו' והכוונה על ברית הזכרים שחתמת בבשרנו וכן תורתך שלמדתנו על למוד הזכרים שבזכות התורה והברית נחלו ישראל את הארץ ועוד שגם הנשים צריכות ללמוד מצות שלהן לידע היאך לעשותן.
Loosely translated: "These days the Minhag is that women also say "for the covenant...", and it refers to the covenant of the Males, upon whose flesh the covenant is signed. And [the same applies to] "for the Torah..." that the Males learn, for in the merit of the Males' Torah and [the Males'] Bris the Jewish people [which includes the woman] merited the Holy Land. Additionally, women also have a commandment to study the Mitzvos [in the Torah] that are pertinent to them, to know how to perform them." (translation & square brackets mine)
That bris does not necessarily mean the one that a young boy gets at the age of 8 days.
It could just be referring to the covenant with Hashem to fulfill all of the commandments.
Possible answer from here [Rabbi Baruch Epstein]:
The reason why women should be obligated in Birchas haMazon (blessings after a meal) is that these are blessings and thanksgiving on the satiation and benefit received by the body. Thus it is obvious that no distinction exists between men and women, since everyone receives the physical benefit. This is similar to the concept that everyone is obligated in the reading of the Megilah since all were involved and benefited from the miracle.
In the Bavli (Berachos 22b) Ravina asks Rava, are women obligated in the mitzvah of Birchas haMazon from the Torah or by rabbinical decree?
Rashi explains the question that this a positive mitzvah that is not time-bound (and thus women are obligated from the Torah), or it is a rabbinical decree since the verse states, על הארץ הטובה אשר נתן לך and women are exempt from the Torah since the land was not given to them (but to the males).
Tosfos writes that since the Birchas haMazon includes the language בריתך שחתמת בבשרנו and ועל תורתך שלמדתנו and women are not able to say those concepts as applying to them.
And on this basis, Poskim decide that women are obligated from a Safek (doubtful if obligated from the Torah or rabbinical decree).
In Birchas HaMazon the practical differences are many: if one is in doubt if already said the Birchas haMazon, or to be motzi (fulfill the obligation of) another (perhaps of a obligated man), etc.