The Hebrew phrase b'rov am hadrat melech (ברב עם הדרת מלך, "in multitudes there is glorification of the king") (Proverbs 14:28) is a principle in Jewish law that recommends that commandments, good deeds, be performed as part of as large a gathering as possible, with the intention of providing greater honor to God.
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Hebrew Bible
Proverbs 14:28 In the multitude of people is the king's glory; but in the want of people is the ruin of the prince. JPS (1917)
Proverbs 14:28 is cited to suggest that it is best, where possible, to make blessings in an assembly of people. Tractate Megillah 27b interprets the "king" of Proverbs 14:28 as the King of Kings, God, and argues for large worship gatherings.
Talmudic examples of application
The Talmud provides many examples of the practical application of this principle. One such example is brought by a Tosefta (B.Berachot 53a) which quotes a situation in which many individuals were gathered together and learning in a study hall when a candle arrived for use in the havdalah prayer that is recited at the end of Shabbat. In such a case, either each individual could recite his own blessing on the fire, or one person can recite the blessing and all of the others can listen and respond amen, thereby fulfilling their obligation to recite the blessing. Whereas the House of Shammai proposed that each person recite their own blessing, the House of Hillel proposed that one person should recite the blessing on behalf of everyone present in fulfillment of the principle of b'rov am hadrat melech. The law follows the latter opinion - such as Ayin Mishpat Ner Mitzvah citing Maimonides.
Another example is in reference to blowing the shofar.(B.Rosh Hashanah 22b) The Mishna (Rosh Hashanah 4:8) mandates that the shofar be blown during the musaf prayer service, and the Gemara, ostensibly providing an explanation to why the shofar is not blown in the earlier shacharit prayer, provides the rationale that inclusion within the musaf prayer is because of the principle of b'rov am hadrat melech, as more people are in the synagogue by the time the congregation has reached musaf. This rationale is immediately debunked, as the Gemara continues to ask why hallel (when recited) is included in shacharit if b'rov am hadrat melech is indeed governing into which prayers the additions are added.