There are four Greek words for love that are important for Christians to understand. They are agape, phileo, storge, and eros. Three of them appear in the Bible.  If we are going to understand the Bible and the biblical world, it is important that we understand what these words mean and how they differ.
The Greek word for sexual love or passionate love is eros, and we get English words such as “erotic.” When eros was used as a proper noun, it referred to the Greek god of love. The Greek word eros does not appear in the biblical text, so we will not spend time on it in this article, but it has had such an impact on English and our view of sexual love that it is important to mention.
The Greek word that refers to the love of God, one of the kinds of love we are to have for people, is agape. Agape is the very nature of God, for God is love (1 John 4:7-12, 16b). The big key to understanding agape is to realize that it can be known from the action it prompts. In fact, we sometimes speak of the “action model” of agape love. People today are accustomed to thinking of love as a feeling, but that is not necessarily the case with agape love. Agape is love because of what it does, not because of how it feels.
God so “loved” (agape) that He gave His Son. It did not feel good to God to do that, but it was the loving thing to do. Christ so loved (agape) that he gave his life. He did not want to die, but he loved, so he did what God required. A mother who loves a sick baby will stay up all night long caring for it, which is not something she wants to do, but is a true act of agape love.
The point is that agape love is not simply an impulse generated from feelings. Rather, agape love is an exercise of the will, a deliberate choice. This is why God can command us to love our enemies (Matt. 5:44; Exod. 23:1-5). He is not commanding us to “have a good feeling” for our enemies, but to act in a loving way toward them. Agape love is related to obedience and commitment, and not necessarily feeling and emotion. “Loving” someone is to obey God on another’s behalf, seeking his or her long-term blessing and profit.
The way to know that we love (agape) God is that we keep His commandments. Jesus said, “Whoever has my commands and obeys them, he is the one who loves me…” (John 14:21a). There are Christians who say they love God, but their lifestyle is contrary to the will of God. These people mistake their feeling of affection for God for true agape love. Jesus made this clear: “He who does not love me will not obey my teaching…” (John 14:24a).
Love is the distinctive character of the Christian life in relation to other Christians and to all humanity. The “loving” thing to do may not always be easy, and true love is not “mushy sentimentalism.” There is often a cost to genuine love. For example, punishing criminals to keep society safe is loving but not easy or pleasant, and asking someone to leave your Christian fellowship because he persists in flagrant sin is loving, but never easy (1 Cor. 5:1-5). That is not to say the agape love cannot have feelings attached to it, and the ideal situation occurs when the loving thing to do also is what we want to do. Christians are to be known for their love to one another (John 13:35).
The third word for “love” we need to examine is phileo, which means “to have a special interest in someone or something, frequently with focus on close association; have affection for, like, consider someone a friend.”  It would probably be helpful if phileo were never translated “love” in the New Testament, because it refers to a strong liking or a strong friendship. Of course, we see how phileo gets translated “love,” because in modern culture we say we “love” things that we strongly like: “I love ice cream,” “I love my car,” “I love the way your hair looks,” etc. The word phileo implies a strong emotional connection, and thus is used of the “love,” or deep friendship, between friends. You can agape your enemies, but you cannot phileo them.
The difference between agape and phileo becomes very clear in John 21:15ff, but unfortunately it is obscured in almost all English translations. After being raised from the dead, Jesus met Peter. Here is the short version of what they said to each other.
Jesus: Simon…do you love (agape) me more than these [fish?].
Peter: Yes, Lord; you know that I love (phileo) you.
Jesus: Simon…do you…love (agape) me?
Peter: Yes, Lord, you know that I love (phileo) you.
Jesus: Simon…do you love (phileo) me?
Peter: [Grieved] “Lord…you know that I love (phileo) you.”
Why the difference in words for “love” in this conversation? Why did Jesus use agape and Peter use phileo? Jesus was asking Peter if he loved him with the love of God, a love that may require sacrifice. After all, Jesus had just gone through horrendous torture for Peter’s sake (and ours), something he did not want to do but did anyway because of his agape love. In contrast, Peter avoided possible torture by denying Jesus.
Jesus twice asked Peter, “Do you agape me? [That is, are you willing to do things for my sake that you do not want to do?]” Peter, on the other hand, still felt the sting of having denied Jesus, and was hopeful that their friendship was intact. Did Jesus hold Peter’s denial against him? Would he still treat Peter as a close associate and companion? Peter was not sure where he stood with Jesus, so he was trying to let Jesus know that he was still a true friend, and had phileo love for Jesus.
The third time Jesus spoke to Peter, he came to Peter’s level and asked if Peter were indeed a true friend (phileo), which grieved Peter. Nevertheless, it was important, because Jesus knew what Peter did not know—that Jesus would ascend into heaven, and Peter and the others would be left to carry out his work on earth, which would require that they all be his good friends and do his will even when it meant hardship.
The fourth Greek word we need to understand is storge, which is the love and affection that naturally occurs between parents and children, can exist between siblings, and exists between husbands and wives in a good marriage. It occurs in Romans 12:10 in the word, philostorgos, which is a compound word made up of philos (the noun form of phileo) and storge. Romans 12:10 is a very important verse, directing us to be very loving and kind to each other.
Romans 12:10 (Author’s expanded translation)
As to your brotherly love, let there be deep friendship and family-affection toward one another.
If one is going to have a wonderful Christian life, obedient to the voice of God and have rich fellowship with other Christians, he or she will need to exercise all three kinds of love. We need agape love because some of the things that God requires of us are not fun or easy, but need to be done. We need to have phileo love because we need true friends to stand with us, people who are emotionally connected to us and with whom we can share our deepest thoughts and feelings. Lastly, we Christians need to have storge love between us, a deep family affection that comforts us and helps us feel connected to all our spiritual family.
 This is a change from our teaching in the past. We have taught that only agape and phileo appear in the Bible, but storge does appear in a compound form in Romans 12:10.
 Arndt, William and F. Gingrich. A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Bibleworks).