If you are truly saved, then you have the Holy Spirit dwelling within you, [1 Cor 12:13] and you become members of Jesus' body [Eph 5:30-32]. His body is called the Church and He is the head of his body [Eph 1:22-23; Col 1:18]. With this being true, the church is to be subject unto Christ [Eph 5:23-24].
This spiritual Church is a living organism of which every born again child of God is a member [2 Cor 12:13-27]. The Holy Spirit gives gifts to each born again believer to fulfill his part in the body so that all believers can function together as one body. This body is the pillar and ground of the truth and is to bring glory to God through the Lord Jesus Christ [1 Tim 3:15, Eph 3:20-21].
Local churches, on the other hand, are organizations. And though they should be made up of born again believers, often they are not. You can be a member of a local church and not be a member of the body of Christ. Likewise, you can be a member of the body of Christ and not be a member of a local church. This is a very distinct difference between local churches and the Church, which is the Lord’s body. Also, there is one Church but there are many local churches [Acts 9:31, 13:1, 14:23, 15:41, etc.].
The job of the local Church is to do the work of God here on earth. This work includes spreading the Gospel of Jesus Christ, and sharing God's love with others. We must remember however that Christ is the head of the local Church and leads through the pastor [1 Pet 5:1-4, 1 Tim 3:1-7]. The pastor is assisted in the ministry by deacons and other helpers [1 Tim 3:8-13, Acts 6:1-4, Rom 16:1-15]. Its members separate from the world to keep worldly influences from hindering its work [2 Cor 6:14-18]. Since it is one body it needs to function in decently and in order without division [1 Cor 1:10-13, 1 Cor 3:1-9]. As you can probably guess, the devil wants to destroy the work and power of the church on earth through corruption of the word [2 Cor 2:17], through division [Rom 16:17-18, through false doctrine [Eph 4:14], and through worldliness [2 Tim 4:3-4].