9 Jesus himself, at the hour of his Passion, prayed "that they may all be one" ( Jn 17:21). This unity, which the Lord has bestowed on his Church and in which he wishes to embrace all people, is not something added on, but stands at the very heart of Christ's mission. Nor is it some secondary attribute of the community of his disciples. Rather, it belongs to the very essence of this community. God wills the Church, because he wills unity, and unity is an expression of the whole depth of his agape . In effect, this unity bestowed by the Holy Spirit does not merely consist in the gathering of people as a collection of individuals. It is a unity constituted by the bonds of the profession of faith, the sacraments and hierarchical communion. The faithful are one because, in the Spirit, they are in communion with the Son and, in him, share in his communion with the Father: "Our fellowship is with the Father and with his Son Jesus Christ" (1 Jn 1:3). For the Catholic Church, then, the communion of Christians is none other than the manifestation in them of the grace by which God makes them sharers in his own communion , which is his eternal life. Christ's words "that they may be one" are thus his prayer to the Father that the Father's plan may be fully accomplished, in such a way that everyone may clearly see "what is the plan of the mystery hidden for ages in God who created all things" ( Eph 3:9). To believe in Christ means to desire unity; to desire unity means to desire the Church; to desire the Church means to desire the communion of grace which corresponds to the Father's plan from all eternity. Such is the meaning of Christ's prayer: "Ut unum sint ".
Source: Ut Unum Sint (Vatican.va)