Order is the appropriate disposition of things equal and unequal, by giving each its proper place (St. Aug., "De civ. Dei," XIX, xiii). Order primarily means a relation. It is used to designate that on which the relation is founded and thus generally means rank (St. Thom., "Suppl.", Q. xxxiv, a.2, ad 4um). In this sense it was applied to clergy and laity (St. Jer., "In Isaiam", XIX, 18; St. Greg. the Great, "Moral.", XXXII, xx).  Order is used to signify not only the particular rank or general status of the clergy, but also the outward action by which they are raised to that status, and thus stands for ordination. It also indicates what differentiates laity from clergy or the various ranks of the clergy, and thus means spiritual power. The Sacrament of Order is the sacrament by which grace and spiritual power for the discharge of ecclesiastical offices are conferred. 

   Grace was attached to this external sign and conferred by it. "I admonish thee, that thou stir up the grace of God which is in thee, through (dia) the imposition of my hands" (II Tim., i, 6). This grace is something permanent, as appears from the words "that thou stir up the grace which is in thee".  The grace then is not a charismatic gift, but a gift of the Holy Spirit for the rightful discharge of official duties. The Sacrament of Order has ever been recognized in the Church as such.
The first effect of the sacrament is an increase of sanctifying grace. With this, there is the sacramental grace which makes the recipient a fit and holy minister in the discharge of his office. As the duties of God's ministers are manifold and onerous, it is in perfect accord with the rulings of God's Providence to confer a special grace on His ministers. The dispensation of sacraments requires grace, and the rightful discharge of sacred offices presupposes a special degree of spiritual excellence. The principal effect of the sacrament is the character (q.v.), a spiritual and indelible mark impressed upon the soul, by which the recipient is distinguished from others, designated as a minister of Christ, and deputed and empowered to perform certain offices of Divine worship (Summa, III, Q. lxiii, a. 2). The sacramental character of order distinguishes the ordained from the laity. It gives the recipient in the diaconate, e.g., the power to minister officially, in the priesthood, the power to offer the Sacrifice and dispense the sacraments, in the episcopate the power to ordain new priests and to confirm the faithful.

(Condensed from: The Catholic Encyclopedia)