Affection is a moderate feeling, tender attachment, or fondness. This portion of Romans 12 says, to "be kindly affectionate in brotherly love." There are 3 types of love mentioned in the bible, agape, phileo, and storge.
Agape love is unconditional love, the kind of love God showed when He sent His Son to die on the cross, "For God so loved the world..."John 3:16. Phileo is brotherly love, it is where we get the word Philadelphia -- The City of Brotherly Love. Storge is the love of parents to their children or the love of siblings.
The words "kindly affectionate" in the verse is a compound word "philostorgos", which most likely means a deep family like friendship. Since as Christians we are part of the family of God that would definitely make since. We are all brothers and sisters in Christ loving each other as a family is important. It was so important that God had it said twice in the same phrase. God wants us to live in harmony with each other, does that mean we will always treat each other this way? No, we are human our pride and selfishness get in the way. Beside who has ever seen siblings who live in complete harmony all the time.
When we do let pride and selfishness get in the way, we are supposed to see it and repent from it. We are then suppose to ask our "siblings" for forgiveness. As Christians we are always supposed to try and live in harmony, being kindly affectionate and loving each other.
Lord, help me to love others the way you want me too with kindly affection and brotherly love. And when I fail to do so please help me to ask for forgiveness from the person and from you.