"And a man will stumble over his brother [which is interpreted to mean] man will stumble because of his brother's iniquity. This teaches that all Jews are responsible for one another (areivin zeh ba-zeh)" (Shavuot 39a).
The principle of areivut teaches that all Jews are bound together in a covenant of mutual responsibility and liability. The fundamental conceptual underpinnings of areivut emerge from consideration of the following halachah. "Ahavah, the son of R. Zeira taught : with regard to all the blessings the rule is that even though one has fulfilled [yatza] his own obligation to recite a particular blessing he can cause others to fulfill [motzi] their obligation to recite that blessing [with the exception of blessings of enjoyment]" (Rosh Hashanah 29a).
This halachah of yatza motzi primo facie contradicts the rule of the mishna that, "whoever is not obligated in a particular matter cannot cause the public to discharge their obligation [vis-a-vis that matter]"(ibid.). Rashi and other Rishonim ad locum reconcile this apparent contradiction by explaining that the mishnah's rule applies to one who was never obligated in the mitzvah. One who was obligated in the mitzvah, however, even after having performed the mitzvah remains obligated by virtue of any other Jew's unfulfilled obligation and need for assistance. The basis for this continuing obligation is the principle of areivut.
Let us briefly analyze this explanation. In order to cause others to fulfill their obligation vis-a-vis a particular mitzvah, one must be obligated in the same mitzvah. Thus it emerges that areivut is not an independent mitzvah or free-standing concept such as loving one's fellow Jew; rather it is an integral internal component of each and every mitzvah. One's personal obligation vis-a-vis any particular mitzvah dictates not only that he individually perform the mitzvah but also that he assist any other Jew in doing the same.
Let us briefly digress and consider the following teaching of Rav Soloveitchik zt"l. The Rav often explained that Judaism conceives of the Jewish nation (as well as any microcosmic Jewish community) not simply as a large aggregate or massive partnership of individuals, but rather as a distinct metaphysical entity. (Vide the Rav's essay "The Community" in Tradition Vol. 17, No. 2 pp. 9-10, Fn. 4. See also Meshech Chochmah on the haftorah of parshat Devarim.)
Upon further reflection, in light of the Rav's teaching, it emerges that the concept of areivut reflects a fundamental Torah principle. Prior to the giving of the Torah, Hashem promises the Jewish People that if they accept the Torah, "you shall be My special treasure among nations...you will be a kingdom of priests and a holy nation to Me," (Exodus 19:5-6). Torah was not given to 600,000+ individuals. Rather, the Torah was given to the Jewish people as a distinct metaphysical entity. Every Jew is derivatively endowed with sanctity (kedushat yisroel) and is obligated in mitzvot by virtue of his or her belonging to the Jewish nation. Mitzvot were given to the Jewish people as a whole and thus the derivative obligation of every individual Jew is to facilitate fulfillment of the mitzvot by all members of the Jewish people - himself as well as others. The principle of areivut which underlies the halachah of yatza motzi encapsulates this fundamental notion.
This concept of the Jewish People as a dictinct metaphysical entity illumines the gemarah's phraseology regarding areivut.The gemarah's phrase areivin zeh ba-zeh is conventionally understood in terms of the primary meaning of the root ayin-reish-bet, to guarantee. Hence the translation, all Jews are guarantors, or responsible for one another. Nonetheless, it seems quite plausible that the phrase should be understood in light of the root's secondary meaning, to mix or blend. And thus, the gemara's apothegm should be understood thus, "all Jews are bound up with each other," expressing not merely mutual responsibility and liability, but existential unity and identity. The use of the "ba'", "areivin zeh ba-zeh" suggests this alternate understanding because in Hebrew idiom when the root ayin-reish-bet connotes guaranteeing it is followed by the propositional letter lamed, and when it connotes mixing it is followed by the propositional letter "bet". [Vide Chidushei ha-Ritva ad locum who apparently advances both interpretations.]
Recognizing the metphysical identity of the Jewish People allows us to fully appreciate the following teaching encoded in the Torah, decoded by our Sages. The Torah describes the Jewish people's journey to Mt. Sinai to receive the Torah. "They had departed from Rephidim and had arrived in the Sinai Desert, camping (vayahanu) in the wilderness. Israel camped (vayehan) opposite the mountain" (exodus 19:2). Our sages (Mechilta ad locum), prompted by the Torah's apparent linguistic inconsistency in shifting from the plural (vayahanu) to the singular (vayehan), comment that when the Jewish people arrived at Mt. Sinai they achieved a remarkable degree of unity, hitherto unattained. They were as, "one person with one heart." (ibid.) Hence the shift from the plural to the singular form of speech. In light of the aforementioned remarks, it is abundantly clear that this remarkable achievement did not coincidentally precede the giving of the Torah. Rather it was a sine qua non for the giving of the Torah to the Jewish people who, unified, emerged as a distinct metaphysical entity. As long as divisions and divisiveness separated Jews, they remained individuals, unworthy of the Torah. The Jewish nation crystallized and became worthy of the Torah when this remarkable state of unity was achieved.
And finally, appreciating the indispensability of Jewish unity to matan Torah provides insight into a famous Talmudic passage. The gemara in Masechet Yevamot records the tragic history of the period spanning Pesach and Shavuot during which time R. Akiva's 24,000 disciples perished "because they did not accord each other proper respect" [as measured by the highest of standards to which they, disciples of R. Akiva, were held] (ibid 62b). Surely, the timing of the divine punishment is not happenstance, but rather is determined in accordance with the sin. Every year between Pesach and Shavuot we prepare ourselves to re-create the giving of the Torah. Reattaining the remarkable unity which was a sine qua non for matan Torah is thus of the highest priority. At a time of hightened sensitivity to and striving for unity, R. Akiva's disciples' interpersonal deficiency was especially egregious and accordingly punished.