The Greek word for sacrificial and selfless love, as distinct from philos and eros. It speaks of one soul being bound up with another. It is a love of commitment and true devotion, and also of sacrifice. It's also truly unconditional, given without expectation of return.
Of the three "types" of love, agape is the hardest to come by and takes the longest to achieve between two people. In marriage, it's the opposite of divorce. In the New Testament, it's the kind of love God has for his human children and sends Jesus to fulfill. If you receive it, you know you never have to question it. And if you give it, you know that it can never be changed, no matter how angry you may be today or yesterday or tomorrow.
Agape is not a "superior" love to philos or eros, though. That would imply that those forms of love are needed first for agape to be present. On the contrary, it's possible to devote yourself to someone you aren't attracted to, and you can be willing to sacrifice yourself for somone you consider an enemy. Unconditional love is possible outside of marriage and God. It's just a lot harder to come by.