This accords with the explanation given in Chassidic discourses (also based on the Torah's "revealed" teachings) that the entire purpose of the soul's descent in this physical world is to progress from a state of omdim, "standing stationary" [with an established and restricted level of service and limited accomplishment] to a state of halichah, "going" [expanding and progressing] and mehalchim, "proceeding" [reaching ever higher levels]. This is expressed (amongst other ways) in an actual, physical parade.
From time to time (during an es razton, a favorable time), we gather and proceed together with the entire community (for we are taught, "Do not segregate yourself from the community"), in order to emphasize and show … that the Jewish people are proceeding … mechayil el chayil, "going from strength to [even greater] strength." (Parshas Behar-Bechukosai, Iyar 8, 11 and 15 5748; Hisvaaduyos pp. 269-270)
A complete Menorah
[On Lag B'omer 5750, during the Parade, the Rebbe explained the significance of Jewish unity at this time: The Jewish people are likened to the seven-branched Menorah of the Beis HaMikdash; there are seven branches of divine service, based on the seven attributes. Now, although each Jew contains aspects of all seven attributes, nevertheless, each Jew's individual divine service is predominantly colored by just one of the seven. Our patriarchs similarly displayed predominant attributes; Avraham symbolized chesed (kindness); Yitzchak, gevurah (severity); and Yaakov, tiferes (beauty).
However, during the counting of the Omer, all Jews address all of these attributes – indicating a unique state of unity, causing the seven branches to visibly unite into a single golden Menorah.
Achdus and chinuch
The Rebbe then continues to explain the relevance to Jewish children in particular (noting that "the Jewish custom (which is a veritable part of Torah) is to specifically celebrate Rashbi's Day of Rejoicing through gathering and uniting Jewish children"): Kindness and brotherhood is one of the basic tenets of Jewish education. This is seen explicitly in the passage in which Hashem speaks in praise of Avraham (Bereishis 18:19), "For I have loved him, because he commands his children and his household after him, that they keep the way of Hashem, doing charity and justice." See Hisvaaduyos p. 192 ff. at length.]
