Romans 12:9-13 meaning

In this continued pursuit of righteousness (harmonious living through faith), Paul tells us to let love be without hypocrisy (v 9). 

The Greek word translated love is "agape," which involves actions focused on benefitting others. We can act in such a way that we think makes us look good, rather than in a way that genuinely serves the best interest of others—this is hypocrisy rather than agape love. 

Agape love is not rooted in emotion, but in value-based choices. Agape love sincerely and honestly seeks to serve others with our gifts, regardless of how we might feel (1 Corinthians 13:4-7). We know from Romans 5:5 that God's love has been given to us through the Holy Spirit. This is the love that Paul is talking about, the same kind of sacrificial love Jesus showed for us, dying for us while we were undeserving sinners (Romans 5:8).

Paul exhorts his audience to abhor what is evil; cling to what is good (v 9). This is necessary to living a holy life as part of the body of Christ. 

This again emphasizes that acting in love is a choice we make. We are admonished to renew our minds. This renewal means we adopt a perspective that it is in our best interest to choose to do good to others as the means by which we best benefit ourselves. This would be true in the present, as we create community harmony with our service and bring blessing to our surroundings. It would also be true in the next life, as great reward goes to those who patiently continue to do good (Romans 2:5-7). 

Within the body of believers, the Church, we should love one another like family, as Paul instructs Be devoted to one another in brotherly love; give preference to one another in honor (v 10). The phrase brotherly love translates the Greek word "philadelphia." This word is from "philo," meaning affection, and "adelphia," meaning brotherly. 

The phrase give preference to one another is interesting. The Greek word translated give preference carries the idea of showing the way. To go before another in order to lead. So the idea seems to be to focus on being a great example for others to follow. Given the immediate context this would mean that Paul desires we focus on showing others how to be a living sacrifice (living to please God), being a great team player, serving diligently with our gifts, and seeking the best for others. 

In verses 10-13, Paul gives us examples of how this brotherly love for each other should look: Be devoted to one another in brotherly love; give preference to one another in honor; not lagging behind in diligence, fervent in spirit, serving the Lord; rejoicing in hope, persevering in tribulation, devoted to prayer, contributing to the needs of the saints, practicing hospitality. 

A pursuit of harmonious living (righteousness) through faith is exampled by brotherly love in the following ways:

• Being a good example in brotherly love looks like being a good example in general, to give preference to one another. 
• Being a good example in brotherly love looks like not lagging behind in diligence in being a good example, in serving with our gifts and in seeking the best for others. 
• Being a good example in brotherly love looks like being fervent in spirit, serving the Lord. The word translated fervent is used only one other time in scripture where it describes Apollos, who is said to be "speaking and teaching accurately the things concerning Jesus." Apollos was missing much of the story, but he was being faithful with what he had and therefore is an example of doing what we can with what we have (Acts 18:25). He was serving the Lord with diligence and enthusiasm. 
• Being a good example in brotherly love looks like rejoicing in hope and persevering in tribulation. It is inferred from context that being a good example of a living sacrifice means enduring trials with joy (James 1:2-3). It means having an unwavering hope that following God's ways will please Him, and lead to our own greatest fulfillment; when we walk in God's ways we fulfill the design for which He created us (Hebrews 11:6). 
• Being a good example in brotherly love looks like being devoted to prayer. The word translated devoted carries the idea of readiness and steadfastness. We are to be ready to pray, and be so in a continuous manner. 
• Being a good example in brotherly love looks like being generous to those in need, contributing to the needs of the saints. This is sharing our material goods with others. 
• Finally, being a good example in brotherly love looks like practicing hospitality. This is sharing our space and time with others. 

Hebrews has a similar list in Chapter 13, and has an interesting mention with respect to hospitality:

"Do not neglect to show hospitality to strangers, for by this some have entertained angels without knowing it."
(Hebrews 13:2)

This reference is likely a remembrance of Abraham entertaining strangers, being hospitable to them, when one of them was the Angel of the Lord who pronounced that Abraham would have a son by Sarah, fulfilling a dream that had been lost to them (Genesis 18:13-14). 

A harmonious life with fellow believers will involve all of these chosen activities, which are all given in the context of being humble, realizing that we are a part of a body. We are each required to contribute to and help others in the body in order to live a life of harmony together as believers. 

All these behaviors are a result of choosing a perspective apart from that of the world, a perspective rooted in the reality of God's design for creation (Romans 12:1-2). When we see the world through the lens of what is true, we realize that being a living sacrifice is the logical way to live. We are most fulfilled when we live according to how God designed us. And God designed us to live in harmony and love with others.