Wayne Grudem says it simply and well: “The church is the community of all true believers for all time.“ The church (Greek ekklesia) is the term used in the New Testament to refer to those who, through faith in the work of Christ, have been united together as one body, an eternal community that transcends time and place and that will one day share perfect fellowship with God forever.
Not only are these people united to one another, but they are united to Christ himself, who is the head of the body (Ephesians 1:22-23; 5:23). Or, to use the marriage analogy Paul introduces in this letter to the Christians at Ephesus, Christ is the husband in the one-flesh relationship between himself and his bride, the church (5:31-32).
This is the global sense of the term church which is used primarily in Ephesians and a few other places in the New Testament (e. g. Matthew 16:18 “on this rock I will build my church”). However, the bulk of the New Testament references to church refer to this community of Christ as it exists in its multiple, diverse, local expressions throughout the world. Paul begins several of his letters, “To the church of God that is in Corinth” or “To the church of the Thessalonians.” And the book of Revelation contains messages to seven particular Christian communities or churches (Revelation 2:1-3:22). So we are right to refer to all Christians as the church and we are right to refer to our local gatherings as churches.
That you belong to the global church implies that you will belong to and be actively involved in a local church as well, for, as Hebrews suggests, your faith and obedience depend on it:
Let us hold fast the confession of our hope without wavering, for he who promised is faithful. And let us consider how to stir up one another to love and good works, not neglecting to meet together, as is the habit of some, but encouraging one another, and all the more as you see the Day drawing near. (Hebrews 10:23-25)