First, the three orders of ordained ministry involve identification with particular aspects of Christian discipleship to which all baptized Christians are called to some degree -- it is just that deacons, priests, and bishops are called to identify with them to a degree that ordinary Christians are not. All are called to serve, as Christ was called to serve, but deacons are called to identify with that servanthood in such a way that their whole life becomes a life of servanthood. All are called to act in priestly ways, but priests are called to identify with Christ as priest and victim in such a way that their whole life becomes a life of priesthood. And bishops, in addition to being "high priests", are called to the ministry of shepherding, of overseeing the church -- and all are called to that ministry to one extent or another, but bishops are called to identify with the church in such a way that their whole life is a life lived for the church.
Specifically, priests are called to be ministers of Word and Sacrament, most especially the Eucharist. All Christians should read and meditate on Scripture, and make the Bible their own book -- but priests are called to so identify with Scripture that they are women and men of the Word, so that it permeates their very being, so that they can preach -- the official sermons during liturgy are when they do this most visibly, but in a sense, there should never be a time in their waking life when they are not (and the dreams of a priest while sleeping should be filled with biblical symbolism). All Christians are called upon to sanctify their daily lives with the presence of Christ, but through the life of constant prayer (the center of which is the Divine Office, with its round of psalms, scripture, and prayer on behalf of the church) in intercession for the church, the priest is called to live out that Incarnation constantly. (While I know that religious do this as well, the Divine Office is more of a means of sanctification for religious, whereas priests and other clergy are more bound to recite it on behalf of the church than as a means of personal sanctification. It is sacrificial.) Finally, with the Eucharist, the priest becomes an "alter Christus", "another Christ", in acting on behalf of Christ as the priest who makes the one sacrifice of Himself on Calvary, and acting with Christ in offering himself or herself on behalf of and in intercession for the world.
Another way of looking at this is to look at where the "home" of each order is. The place of ministry for the laity is in the world. When they come to church, they sit in the nave, and are the ones who receive ministry. Laity do not come to church to minister, but to be ministered to, so that they can return to the world to minister. The place of ministry for the deacon is at the threshold -- during the week, near the door of the church, acting to communicate between church and world. The place of the deacon during the liturgy of the word is at the crossing, between the nave and the chancel, proclaiming the gospel facing the people, leading the intercessions facing the altar. The place of the deacon during the liturgy of the Eucharist is at the altar, assisting the priest. The place of the priests during the week is in the church, ministering to those who come for solace and ministry. Their place in the liturgy is in the pulpit and at the altar. The bishop, as a priest, belongs in those places as well, but also at the cathedra, overseeing the whole operation. Joseph described it thus at the gathering with the clergy -- God owns the restaurant, the bishop is the manager, the priests are the chefs, the deacons are the waiters, assisted by the minor order busboys, and the laity are the customers who come to eat.