The word “Church” (Latin ecclesia, from the Greek ek-ka-lein, to “call out of”) means a convocation or an assembly. It designates the assemblies of the people, usually for a religious purpose. [Cf. Acts 19:39] Ekklesia is used frequently in the Greek Old Testament for the assembly of the Chosen People before God, above all for their assembly on Mount Sinai where Israel received the Law and was established by God as his holy people. [Cf. Ex 19] By calling itself “Church,” the first community of Christian believers recognized itself as heir to that assembly. In the Church, God is “calling together” his people from all the ends of the earth. The equivalent Greek term Kyriake, from which the English word Church and the German Kirche are derived, means “what belongs to the Lord.”
In Christian usage, the word “church” designates the liturgical assembly, [Cf. 1 Cor 11:18; 14:19, 28, 34, 35] but also the local community [Cf. 1 Cor 1:2; 16:1] or the whole universal community of believers. [Cf. 1 Cor 15:9; Gal 1:13; Phil 3:6] These three meanings are inseparable. “The Church” is the People that God gathers in the whole world. She exists in local communities and is made real as a liturgical, above all a Eucharistic, assembly. She draws her life from the word and the Body of Christ and so herself becomes Christ’s Body. (CCC 751-752)
“The People that God gathers in the whole world” is a true reflection of the meaning of catholicity or “universality,” a “totality,” “a keeping with the whole.” This is expressed in a two-fold manner:
830 . . First, the Church is catholic because Christ is present in her. “Where there is Christ Jesus, there is the Catholic Church.” [St. Ignatius of Antioch, Ad Smyrn. 8, 2: Apostolic Fathers, II/2, 311] In her subsists the fullness of Christ’s body united with its head; this implies that she receives from him “the fullness of the means of salvation” [UR 3; AG 6; Eph 1:22-23] which he has willed: correct and complete confession of faith, full sacramental life, and ordained ministry in apostolic succession. The Church was, in this fundamental sense, catholic on the day of Pentecost [Cf. AG 4] and will always be so until the day of the Parousia. [795, 815-816]
831 Secondly, the Church is catholic because she has been sent out by Christ on a mission to the whole of the human race: [Cf. Mt 28:19] [849, 360, 518]
All men are called to belong to the new People of God. This People, therefore, while remaining one and only one, is to be spread throughout the whole world and to all ages in order that the design of God’s will may be fulfilled: he made human nature one in the beginning and has decreed that all his children who were scattered should be finally gathered together as one…. The character of universality which adorns the People of God is a gift from the Lord himself whereby the Catholic Church ceaselessly and efficaciously seeks for the return of all humanity and all its goods, under Christ the Head in the unity of his Spirit. [LG 13 ## 1-2; cf. Jn 11:52]
Source: Catechism of the Catholic Church para. 751-752, 830-835.