2 Peter 1:5 says that our faith is to be supplied with virtue. We must not have a faith that makes a good profession, but then is betrayed by bad character or bad behavior. A good faith must be clothed with goodness of heart and life.
Paul's letter to the Philippian believers provides instruction on this subject of virtue. Most helpful is the constellation of seven characteristics in Philippians 4:8:
Finally, brethren, whatever is true, whatever is honorable, whatever is right, whatever is pure, whatever is lovely, whatever is of good repute, if there is any excellence and if anything worthy of praise, dwell on these things.
The 6th characteristic, "excellence," translates the same Greek word for "virtue in 2 Peter 1:5. The closest companion-term to "excellence" in the list is "worthy of praise." Our professed faith is to be accompanied by a praise-worthy life. Yes, we are all sinners, and we disappoint in so many ways. But Peter would have us exercise diligence in cultivating a life that has this kind of fruit, and not leave our faith fallow, as though it were a bare field.
But aside from this key parallel text that helps us understand the idea of "virtue" in 2 Peter 1:5, there are other references in Philippians that help out as well. A hint of this is provided in the opening verses, where Paul reminds us that God has begun a "good" work in us (1:6). He has planted the seed of Christian virtue in our new lives. That seed must grow, and we are to encourage its growth. Now let's look at some material from each of the first 3 chapters.
Paul prays for the believers in Philippians 1:9-11. The shape of virtue that is sought in this prayer is a discerning love that grows in excellence (different word from 2 Peter 1:5, though similar concept) and is marked by sincerity and blamelessness, not for the sake of this world, but for the sake of the Lord. We hope for and work toward a righteous fruit. There are major aspects of this process for which have little responsibility or capability. There are certain things that only God can do. But we are to develop a taste and sharpen an appreciation, not for base or crude things, but for the kinds of things with which God is pleased, and for the kinds of things that will be fitting on the last day and in the light of God's glory. Paul is praying for a kind of virtue that shines brightest in heaven's light, whether or not it wins much of the world's acclaim.
Humility is a key element in Christian virtue in Philippians 2 (verse 3 and surrounding context). While self-concept and self-confidence are key components in this world's definition of virtue, humility is just as necessary for heaven's definition. Paul uses a most strong support for humility by appealing to the incarnation/passion of Christ, in which he humbled himself. Perfect Christian virtue is found in Christ. Christ was humble. It cannot be missing from the expression of our faith. A proud Christian has a virtue problem.
Finally, I want to emphasize that Christian virtue is different from common virtue. Common character qualities are admirable and desirable. But, outside of Christ, there is often a quest to do good or to be good enough in order to offset the bad that we are or do. This is not Christian. The Gospel (Good News) is that sinners (all of us) may receive and benefit from salvation by faith - not in ourselves, but by faith in Christ, the only truly Faithful One and Righteous One. So the final aspect of virtue in Philippians that I would have you consider is Paul's aspiration in 3:7-11 - knowing Jesus in such a way that we are identified with him; identified with him in such a way that his death and resurrection are actually integrated into our lives. We are bound up with him. His death kills sin and death in us. His life births new, spiritual life in us. All things are from Christ, and for Christ. I am not virtuous because of my virtues. He is my virtue.