Agape is one of four Greek words translated into English as "love." (The other three are "storge" and "philos" and "eros").
Agape is usually understood as a spiritual or compassionate form of love in contrast to the thought of storge which is the deeply affectionate love of family and more broadly the patriotic love of country and can include Agape, and philos which is a brotherly sort of love of close friendship, and eros which is erotic or sexual love.
In descending order of excellence the four loves are:
Agapeo: Unconditional love; the love of God in the renewed mind coming forth in outward manifestation
Storge: Love of family; Parent/child, siblings, cousins, etc.; patriotic love of one's country and people. In a very close family, agape is felt as well
Phileo: Love between friends
Eros: The sense of being in love; romantic love; also the love of pleasant things that provide sensual enjoyment
In the Koine Greek texts of the New Testament, the word agape is used in many places to refer to the love of God, the love of Christ and the living love of the Holy Spirit that unites all men in brotherhood. Most references to it are in 1 Corinthians 13:1-13, where it is referred to as a form of compassion which is unconditional and voluntary; that is, it does not discriminate, is not conditioned by any outside forces, and is something that one decides to do, without thought of personal reward. It is mentioned by Paul again in 1 John 4:8, where it is stated that 'God is love' (ἀγαπη).
Agape, however, is not exclusively divine love. Jesus described the two most important commandments as 'love (ἀγαπη) the Lord your God with all your heart and with all your soul and with all your mind' and 'love (ἀγαπη) your neighbor as yourself', in Matthew 22:37-41
Agape is what one could call Christian or brotherly love, and by its very nature it is selfless and giving. One must consider that the selfless agape love is the love that people of the Christian faith are to have for one another, as Christ would have had for them.