When you fall in love, you're suddenly, powerfully attracted to someone. You might dream that you'll travel to Paris someday and fall in love with a beautiful French woman.
The moment when you pass from a state of being friends with a person to loving him in a romantic way is when you fall in love. For some people, that happens once in a lifetime — others fall in love over and over again. Fall in love has been around since at least the 1500's, and it comes from the sense of fall that means "occur or become apparent, especially suddenly." Other similar phrases are fall asleep or fall behind.