While discussing the blessings that accompany the recitation of the Shema, the Gemara describes the practice in the Temple. In a Mishna in Massekhet Tamid we learn:
In the morning the deputy High Priest appointed to oversee activity in the Temple, said to the priests who were members of the priestly watch [mishmar] on duty that week: Recite a single blessing. The members of the priestly watch recited a blessing, and read the Ten Commandments, Shema, VeHaya im Shamoa and VaYomer, the standard recitation of Shema. Additionally they blessed the people with three blessings. These blessings were:
True and Firm, the blessing of redemption recited after Shema;
Avoda, service, the special blessing recited over God’s acceptance of the sacrifices with favor, similar to the blessing of Temple Service recited in the Amida prayer; and
the priestly benediction, recited in the form of a prayer without the outstretched hands that usually accompany that blessing.
And on Shabbat one blessing is added to bless the outgoing priestly watch, as the watch serving in the Temple was replaced on Shabbat.
Even before the Temple’s construction was completed, there were already more priests than necessary to perform the sacred service. Therefore, King David and the prophet Samuel established priestly watches (see I Divrei HaYamim Chapter 24). Based on ancient criteria, the priests were grouped into twenty-four watches, each serving in the Temple for one week twice a year. Only during the Pilgrimage Festivals, when the entire nation ascended to Jerusalem, did all of the priests come to the Temple. During the Second Temple period, the watches were redivided; however, the basic divisions remained intact. Each watch was divided into six paternal families, each assigned to one day of the week, so that all of the members of the watch would serve. The changing of the watches took place each Shabbat, and they would then perform the ceremony and recite the blessing for the incoming priestly watch.
The Gemara teaches that the final blessing that was added when the priestly watch changed over was “May He cause love and brotherhood, peace and camaraderie to dwell among you.”
The Maharsha explains that the incoming priestly watch was blessed with this particular blessing because, at least for a brief period, the choice of the priest who would perform a particular service in the Temple was based on the result of competition between the priests. This competition sometimes led to calamitous results. Therefore, this blessing was recited in the hope that the incoming watch would be blessed with brotherhood and peace.