What is love? Many poets, songwriters, and philosophers have dealt with, and continue to deal with, this question.
Agape is the most common word for love in the New Testament second only to phileo. This word is usually rendered into English as love or as charity in older translations. What is interesting about this word is that in classical Greek, this word is rarely used. In fact, it is a rather colorless word. The favorite word for love for classical Greek writers is phileo, which usually denotes affection and devoted friendship.
The Greeks wrote a lot about love, and used several words to denote the various "types" of love.
There is eros, which denotes a natural attraction. Our English word, "erotic," comes from this. This word is not used in the New Testament.
There is also storge, which usually denotes a family type of attachment and love. This is used only once in the New Testament in a compound word, philostorgos, in Rom. 12:10, and is usually translated, be tenderly affectioned (ASV), be devoted (NASB), or be kindly affectionate (NKJV), or simply, love (RSV, NRSV). There is phileo, which simply means love in the sense of affection or friendship. This word is used many times in the New Testament in many forms and in several compound words. Some examples of compound words are: philadelphia - brotherly love, philanthropia - love for mankind, philos - beloved one or friend, philema - token of affection, usually a kiss, philia - friendship, philoxenia - love of strangers or hospitality, etc…
Then there is agape. Originally, this was a generic word for love and was basically a colorless word. As a result, classical secular Greek writers did not like to use this word. It simply wasn't as expressive or precise as some of the other words at their disposal. By New Testament times, agape eventually became almost a synonym to phileo.
But what is interesting is that the New Testament writers favored agape and went so far as to give it a particular Christian meaning. Agape became the favorite word to describe God's love. Of course agape wasn't used without exception for God's love (Titus 3:5 uses philanthropia for God's love for mankind), but became the usual term for God's love, such as in John 3:16. John says that we know agape by this, that Jesus laid down His life for us (1 John 3:16). He also says that God IS agape (1 John 4:8).
So, when Paul describes agape in 1 Corinthians 13:4-8, he is describing God's love. God is patient, kind, etc… Agape is the richest, most noble kind of love. It is God's love. As a result, Paul concluded, "agape never fails." Since God is agape, He never fails. This is the kind of love we should ultimately have for each other. Agape should be the basis of all the other types of loves we have, whether it is with our wife or a friend. So whether it is in our relationship with God, with the brethren, in marriage, parenting, family, or friends, if we have agape in our heart, we will never fail.