When ten Jews are engaged in Torah or prayer, the Shechinah dwells among them, as it says (Psalms 82:1), “God is present in a Godly congregation.” Although the Shechinah dwells even with one Jew who prays or learns individually, nevertheless, different levels exist. The highest level is when ten Jews are engaged in a matter of sanctity (davar shebikedushah), for then holiness is revealed to the world (see Berachot 6a). Based on this, the Chachamim established that all matters of sanctity be recited in a minyan. These include: Chazarat HaShatz (the repetition of the Amidah), Birkat Kohanim (the priestly blessing), Barchu, Kaddish, and the Torah reading (Megillah 23b).
The Chachamim state that a prayer recited together with the congregation (b’tzibur) is accepted, as is written (Psalms 55:19), “He redeems me unharmed from the battle against me, for those with me are many.” Even when a congregation prays without full kavanah, HaKadosh Baruch Hu does not turn away from the prayers of the many (Berachot 8a). Although any prayer recited amongst ten Jews is more meaningful and accepted, the essence of communal prayer is ten Jews jointly praying the Shemoneh Esrei, also known as the Amidah.
Hence, praying in a minyan provides two benefits: first, in a minyan one may recite all those matters of sanctity that the Chachamim instituted; second, communal prayer is accepted on the merit of the congregation.
Since the Shechinah dwells in the midst of a minyan, every person should try to be one of the first ten people to arrive for prayer. If a person cannot be one of the first ten people to arrive for Shacharit, he should try to be one of the first for Minchah or Ma’ariv (Shulchan Aruch, 90:14; Ben Ish Chai, Miketz 1).
The Mabit in Beit Elokim, Sha’ar HaYesodot, chapter 39, explains that from the time of Moshe Rabbeinu until the destruction of the Temple, wherever sacrifices were brought the Shechinah was revealed and there was prophecy among Israel; therefore, even the prayer of an individual was heard. After the destruction of the First Temple and sacrifices were no longer brought, Anshei Knesset HaGedolah instituted praying in a minyan so that the Shechinah would dwell among them, thereby facilitating the acceptance of their prayers.