He is required to have a pleasant voice and appearance, to be married, to have a beard, to be fully familiar with the liturgy, to be of blameless character, and to be acceptable in all other respects to the members of the community.
Shulchan Aruch [16th c.], Orach Chayim 53:4ff
[His mission] is to lead in prayer. ... He stands before the Ark not as an individual, but with a congregation. He must identify himself with the congregation. His task is to represent as well as to inspire a community. ... [His] function is to help us to live through a moment of confrontation with the presence of God; to expose ourselves to God in praise, in self-scrutiny, and in hope.
Rabbi Abraham Joshua Heschel
The sages asked: Whom shall we appoint to succeed Rabban Gamliel [as the head of the Academy]? ... Let us appoint Rabbi Elazar ben Azariah, for he is wise, and he is wealthy, and he is a tenth-generation descendant of Ezra the Scribe. ...
So they came and said to him: Will it please the master to become the head of the Academy? He said to them: I will go and consult with my family. And he went and consulted with his wife. She said to him: But perhaps they will depose you as well! He said to her: If a person uses a valuable goblet one day, it may well break the next. She said to him: But you have no gray hair! And that day, a miracle occurred and eighteen rows of his hair turned gray. ...
On the day they appointed Rabbi Elazar, they removed the guard from the study hall and allowed anyone who wished to enter. When Rabban Gamliel was in charge, he used to say: Anyone whose inside does not match his outside may not enter this study hall!
Babylonian Talmud, Tractate Berachot 27b-28a
It is simply this: The synagogue is the consequence and not the cause of Jewish life. The synagogue cannot be the surrogate of Jewish life because then you will stultify it, you will freeze it into sanctuary Judaism.
My zedah came to the shul because he was a Jew; his grandchildren come to the temple to become Jewish, but it can't be done in the sanctuary because nothing Jewish will happen inside the sanctuary until something Jewish happens outside the sanctuary. ... Kierkegaard told of the man who passed a store in which it said, "We press suits here." And he brought his suits into the store and the proprietor said, "You made a tremendous mistake; we don't press suits here; we only make signs."
Rabbi Harold Schulweis, "Changing Models of the Synagogue and the Rabbi's Role"
(ד) רבי אלעזר אזל לחד אתר אמרו ליה: פרוס על שמע. אמר להן: לינא חכם. עבור לפני התיבה. אמר להן: לינא חכם. אמרין: דין הוא ר' אלעזר דין הוא דאתון מתגלגלין ביה על מגן צווחין ליה רבי?! נתכרכמו פניו והלך לו אצל ר' עקיבא רבו. אמר ליה: למה פניך חולניות? תני ליה עובדא. א"ל: צבי מרי דיליף? (האם אדוני רוצה ללמוד ממני?) א"ל: אין. אלפיה. לבתר יומין אזל לההוא אתרא. אמרו ליה: פרוס על שמע פרס. עבור לפני התיבה עבר. אמרין: איתחסם ר' אלעזר וקורין ליה: רבי אלעזר חסמא:
Once, Rabbi Elazar came to a certain place, and they said to him: "Lead us in the Sh'ma!" He said to them: "I cannot." They said to him: "Lead us in the morning prayers!" He said to them: "I cannot." They said to him: "Is this really the Rabbi Elazar everyone makes such a fuss about? Why does he even merit the title 'Rabbi'?"
His face fell and he went to his teacher Rabbi Akiva. He said to him: "Why do you look unwell?" and he told him what had happened. He said to him, "Will my master consent to learn from me?" He said to him: "Yes," and so he taught him.
Some time later, he returned to the same place. They said to him, "Lead us in the Sh'ma," and he led them. They said to him: "Lead us in the morning prayers," and he led them.
And they said: "Rabbi Elazar is 'itchasam,'" and they called him "Rabbi Elazar, the Solid One."