First of all, it's important to understand that the Catholic Church does not believe that there has been, nor will be, any new public revelation from God since the Ascension of Jesus; Jesus was "God's Last Word", the full and perfect Word of God. (Perhaps this is what you meant by saying "the Catholic Church believes that there is no direct revelation from heaven to lead the church"?)
Though there have been some private revelations to individuals or groups, and many claimed revelations, none of these belong to the "deposit of faith"—the knowledge and teachings which the Church believes to be divinely sourced and definitively true. This latter kind of knowledge is the revelation of the Word of God Jesus Christ.
This revelation is complete—again, as the Catechism says (quoting St. John of the Cross):
In giving us his Son, his only Word (for he possesses no other), he spoke everything to us at once in this sole Word—and he has no more to say... because what he spoke before to the prophets in parts, he has now spoken all at once by giving us the All Who is His Son.
(St. John of the Cross, The Ascent of Mount Carmel, 2, 22, 3-5; quoted in Catechism of the Catholic Church paragraph 65)
But though the revelation is complete, the interpretation of what has been revealed to us in and through Christ is ongoing:
even if Revelation is already complete, it has not been made completely explicit; it remains for Christian faith gradually to grasp its full significance over the course of the centuries.
(Catechism, paragraph 66)
In Catholic understanding, tradition is a part of revelation, just as scripture is. The Gospels and the rest of the New Testament were written down to preserve the message the Church received from Christ; but in addition the apostles handed on
by the spoken word of their preaching, by the example they gave, by the institutions they established, what they themselves had received—whether from the lips of Christ, from his way of life and his works, or whether they had learned it at the prompting of the Holy Spirit.
(Dei Verbum section 7, quoted in Catechism of the Catholic Church paragraph 76. Dei Verbum is the Dogmatic Constitution [teaching and doctrinal document] on Divine Revelation promulgated by the Second Vatican Council in 1965.)
This orally transmitted part of revelation has come down, the Church believes, directly from the apostles:
"In order that the full and living Gospel might always be preserved in the Church the apostles left bishops as their successors. They gave them 'their own position of teaching authority.'" Indeed, "the apostolic preaching, which is expressed in a special way in the inspired books, was to be preserved in a continuous line of succession until the end of time." This living transmission, accomplished in the Holy Spirit, is called Tradition, since it is distinct from Sacred Scripture, though closely connected to it.
(Catechism of the Catholic Church, paragraphs 77–78; the quotations are from Dei Verbum again.)
Thus this Tradition is more than just "passed down from one man to another"; it's passed down from the Lord Himself, and from His Apostles, by their divinely instituted teaching authority, and its truth is preserved by the oversight of the Holy Spirit. Through the passing down of this tradition from Jesus, the Holy Spirit remains present and alive in the Church:
The Father’s self-communication made through his Word in the Holy Spirit, remains present and active in the Church: "God, who spoke in the past, continues to converse with the Spouse of his beloved Son. And the Holy Spirit, through whom the living voice of the Gospel rings out in the Church—and through her in the world—leads believers to the full truth, and makes the Word of Christ dwell in them in all its richness."
(Catechism of the Catholic Church, paragraph 79. The quotation is from Dei Verbum section 8.)
Thus tradition, as one part of the Deposit of Faith, is a source of our understanding of God:
"Sacred Tradition and Sacred Scripture make up a single sacred deposit of the Word of God" (Dei Verbum 10), in which, as in a mirror, the pilgrim Church contemplates God, the source of all her riches.
(Catechism of the Catholic Church, paragraph 97)