Two pearl fishers in Ceylon (Sri Lanka) meet each other and reminisce about their shared past, where they both fell in love with the same woman. They revitalise their friendship with drinking and singing, to conclude that they will be friends forever. You guessed it: of course they meet the woman they’re singing about, and things are going downhill from there.
That duet is the best known in opera history. It is also one of the few places where it is a duet that is the famous melody of the opera. Usually it is an aria (sung alone), or a choral (sung by the choir). The opera premiered in 1863 in Paris, and was not received very well. About the only critic that was giving the young Bizet the benefit of the doubt was his countryman Hector Berlioz.
I visited Sri Lanka, and although there were some beautiful women there, I never saw any pearl fishers. I doubt Bizet has been there, but he just chose it as a nice exoticism.