If we think unity is for and about us, then we will miss this message. Paul's purpose in this challenge for unity in the local church was not to indulge us in the warmth of brotherly love, but to impact the world’s opinion of God. Glorify means, “to influence one’s opinion about another so as to enhance the latter’s reputation.” BDAG
Unity, day in and day out, among people of diverse backgrounds gives a credible context to what we want the world to know about God. Paul was not simply promoting a worship service where the worshipers publicly speak pleasant things about God. In this passage he was promoting consistent like mindedness as a context to evangelism.
When we experience disunity in our church the direct result is a weakening of our ability to influence the world’s opinion of our Savior. The first work of the evangelist is to secure the unity of his church. It is the anti-evangelist who foments and sows discord. The person who would glorify God must be trained in and use the methods taught in scripture to resolve conflicts and disunity, so God may be truly glorified.