The first Posuk in this week's Parsha states: "ויקהל משה את כל עדת בני ישראל..." "And Moshe assembled the entire congregation of the children of Israel..." (שמות ל"ה:ה'), and we are then told that he informed them about some details concerning the observance of Shabbos. One might ask why the Torah had to stress that Moshe assembled all the people when giving them the Mitzvah of Shabbos. Apparently, it was necessary for Shabbos to be discussed in public, so that everyone would know about it, because Shabbos is described elsewhere in the Torah as a "ברית עולם," a sign of Hashem's eternal covenant (ברית) with Bnai Yisrael (שם ל"א:ט"ז). Something identified as a covenant needs the presence of a large assembly for the purpose of publicizing it, so that all who are a part of the covenant are aware of all its details. One can perhaps suggest that similarly, all other signs of Hashem's covenant which we find in the Torah should also be done in public.
For this reason, perhaps, the Mitzvah of Bris Milah, circumcision, is normally performed at a festive gathering with many people present. For at the Bris Milah ceremony, the entire congregation calls out "כשם שנכנס לברית כן יכנס לתורה לחופה ולמעשים טובים," "Just as he has entered into the covenant, so may he enter into the Torah, the marriage canopy, and good deeds." This formula proclaims the terms of the covenant between Hashem on one side and the newly circumcised infant on the other; namely, that he is expected to learn Torah and serve Hashem, to marry and raise a family in the way of the Torah, and to perform good deeds. If one fulfills this, Hashem will enter that person into the Bris, and he will be entitled to all the benefits of being a part of Hashem's chosen nation. Because this is a covenant, it is done in public, as others who are already part of it welcome the newest member.