The sages of the Talmud, as interpreted by Rabbi Yosef Karo's 16th-century Code of Jewish Law, set down three criteria for male conversion, the latter two applying to females as well: circumcision, immersion in a mikve (ritual bath), and the acceptance of the commandments (Shulhan Aruch, Yoreh Deah, 268, 3). The removal of the foreskin connotes the casting off of gentiledom, and symbolizes the separation of the Jew from the licentious practices (especially in the sexual realm) which characterized the pagan world. (Interestingly enough, the rabbinic sages understood women as "naturally circumcised"). Ritual immersion represents a legal and spiritual rebirth into a new family-nation - after all, every fetus is encompassed in fluid, and birth is heralded by the breaking of the mother's water. (A similar ritual was adopted by Christianity in the form of baptism.) And acceptance of the commandments signals the entry into a religion - a faith community bound together by common adherence to a network of ritual, moral and ethical laws.
So it becomes clear that we are a nation as well as a religion, a nation with its own language, culture and homeland, and a religion with a unique code of law defining our prayer rituals, feasts and fasts, life-cycle celebrations and ethical behavior.
Fascinatingly, the Torah records just such a process of development, a "national conversion," as it were, in the portions we are now reading. By participating in the Exodus from Egypt, the Israelites were separating themselves from the Egyptians, the Egyptian enslavement, the Egyptian concept of slavery as a societal norm, and from the immoral Egyptian lifestyle. And the Torah suggests that the Jews symbolized this removal from pagandom with circumcision, since the Paschal lamb can only be eaten by one who is circumcised (Exodus 12:48).
Precisely when did the circumcision take place? The Torah describes the Israelite preparation for the Exodus, commanding each household to take a lamb on the 10th of Nissan, to guard it until the 14th of the month, and then to sacrifice it to God (which in itself amounted to a disavowal of Egyptian idolatry, since the lamb was one of the Egyptian gods) and place its blood on their doorposts. On the night of the 15th they were to eat the lamb - the first Seder - and then exit from Egypt.
The Midrash asks: Why take the lamb on the 10th and wait until the 14th to sacrifice it? It answers that the male Israelites were to have themselves circumcised during this time, and by merit of the twofold blood - of the sacrifice and the circumcision - they would be found worthy to be freed from Egypt. (Exodus 12:6, Mechilta and Rashi ad loc). Indeed, in Temple times, a male convert would be expected not only to have himself circumcised, but to bring a sacrificial offering as well (Maimonides, Laws of Forbidden Relationships, 13,1).
The ritual immersion of the Israelites took place just before the Revelation at Sinai, either when God commanded Moses to see that the people be "sanctified [through ritual immersion] and their clothing be washed" (Exodus 19:10, see Maimonides, Laws of Forbidden Relationships, 13, 2-3), or when the Israelites jumped into the Reed Sea before it split ("and the children of Israel entered into the midst of the waters on the dry land..." Exodus 14:22). And of course the acceptance of the commandments came following the Decalogue: "...And the entire nation responded with one voice and declared... 'All that the Lord has spoken, we shall do and we shall internalize'" (Exodus 24:3,7).
Indeed, prior to the formula of acceptance, the Torah not only recorded the Ten Commandments as well as the major civil and ritual laws, but also outlined the eventual borders of the Land of Israel (Exodus 23:20-25). In effect, therefore, the Israelites were accepting both Jewish nationality and the Jewish religion. We were to be bound together (am, im) by common genes, land and destiny, as well as by a unifying system of laws, values and lifestyle.