Tradition is the teaching and faith which the Christian Church has passed down from generation to generation; it is also called "Apostolic Tradition" because it is the preserved teaching received from Christ and His apostles since the foundation of the Church.
That is, at least, a somewhat simplistic answer of how Orthodox, Catholics (and etc) generally understand Tradition (with a capital 'T'). Protestants, such as myself, have varying understandings of Tradition based roughly on how our respective denominations and theologies understand it. For instance, I believe Tradition is invaluable but not infallible, to be respected by not regard as beyond reproach.
It is also necessary to note that there is a distinction between Tradition ("Sacred Tradition"/"Apostolic Tradition") and tradition. The Doctrine of the Trinity is Tradition, folding one's hands during prayer is a tradition.
And as for the Church, in includes clergy, but it's the whole Church: all of the Faithful who are members of the Church. For Orthodox it means the Orthodox Church, as they understand that Christ established His Church and sent out His Apostles who preached Him, who established communities pastored by bishops and priests who carry on the Apostles' mission of pastoring and preaching. Catholics believe similarly but believe that among Christ's apostles Peter was the visible head, and thus the successor of Peter remains the visible head, which is the Bishop of Rome also called the Pope. Protestants have various ideas of the Church.
But all those differences aside, what is not meant is simply some clerical authoritarianism, but rather the universal consensus of Faithful Christians who are in communion as one Church, sharing in that faith as preserved for us--either in Scripture alone (as some say) or in Scripture and Tradition (as others say) or in some sort of combination (as still others say). Which is all a very elaborate way of saying that the Church is fundamentally a community (not just a community, but it is a community), the Church is both clergy and laity in concert sharing in faith and living together corporately as a people devoted to Jesus.
-CryptoLutheran