Focusing on Christ's relationship to the church, Paul notes that Christ's goal as the church's husband is to "present the church to himself in splendor." Christ desires the church to stand before Him in brilliance and triumph. His desire is for believers to one day appear before Him without any flaws or marks or imperfections. Particularly on the wedding day, a bride seeks to look her absolute best for her husband, and Christ wants the church to look its best for Him when that day comes. 

The purpose of Christ's relationship with the church is to bring on greater holiness. The reference to blemishes is not about physical appearance, but about the church Is being pure before the Lord. To be holy is to be set apart. To be "without blemish" is to be without a mark or problem. This is the same standard the Old Testament required of animals used in sacrificial offerings. They could not have any "blemish." God desires we come before Him with a clean heart (Psalm 24:4).