It's the desire for a person to be happy, and being happy because of them.
When you love a person, offenses become more hurtful, and good things become much better. Sex with that person is better simply because you love them. There is a deep caring about what happens to that person, and what they want, need, and feel. Being in their presence, talking to them, and remembering good times with them makes you happy, as does the knowledge that they are happy. Every emotion is driven to the extreme, be it happy, sad, or angry. Love doesn't make a damn bit of sense, but it has the potential to be the one thing that makes life most fulfilling.
It's also almost impossible to find, and not worth the pain and suffering you endure in the meantime and as a result, so why fucking bother?