You will eat and be satisfied and bless God. (Deuteronomy 8:10)
Unlike the simple explanation that this verse refers to reciting birkat hamazon (the blessing following a meal which included bread), the Jerusalem Talmud (Berachot 7:7) understands that while birkat hamazon is certainly necessary, this verse refers to zimun, the invitation before reciting birkat hamazon required when at least three men eat a meal with bread together (Chief Rabbi’s Siddur page 758). While Rabbi Avrohom Yeshaya Karelitz, (known as the Chazon Ish, d. 1953) ruled that zimun is a Torah obligation, most other authorities rule that it is rabbinic in nature.
According to the Shulchan Aruch (code of Jewish Law written in 1565), if two people sit down for a meal (with bread) and are joined by a third, provided the third person eats a significant amount of food (Orach Chaim 197:3). This includes a case where the third person drank wine or fruit juice (ibid. 197:2).Some include other drinks but the majority and most notably, Rabbi Yisrael Meir HaKohen Kagen (known as the Chofetz Chaim, d. 1933) do not include drinking water (Mishnah Berurah 197:12).
Everyone who eats together has an obligation to partake in zimun even though only one person leads it. If someone needs to leave the group early it is not acceptable to recite birkat hamazon alone without zimun. In such a scenario the one who wishes to leave should recite zimun together with the first blessing of bikat hamazon out loud and then continue quietly. This satisfies everyone’s obligation.
The Cofetz Chaim also notes that zimun can only be recited when the group either sit at the same table or are of the same household (Mishnah Berurah 193:18). In addition, Rabbi Yosef Shalom Elyashiv (d. 2012) ruled that when a large group come to eat together but at different tables (such as at a simcha) zimun may be recited for the whole group provided the tables are relatively close together (Biur Halacha 167:11).
The act of joining others to thank God for the food we have eaten resonates with the verse in Psalms (34:4) and helps to magnify God’s greatness together.