The meaning is that the person was feeling extremely happy.

Hello Jesús, how have you been? Here we go, Top of the world means that you feel like you are at the highest peak at a mountain just as if you had conquered the whole world. I would compare it to Jack Dawson in Titanic, shouting: "I'm the king of the earth" thus expressing that his joy is overwhelmingly extraordinary. Well, did I exaggerate here? Only the native ones will tell here lol. Cheers buddy!

It means he was feeling wonderful. Here's a song about it: https://www.youtube.com/watch?v=PDc6FtyMg54 I'm sitting on top of the world, I'm rolling along, rolling along; I'm quitting the blues of the world, I'm singing a song, yes, singing a song...

Quiere decir que te sientes muy feliz. Es una metáfora, compara este sentimiento con la sensación que tendriás si hubieras alcanzado la cumbre de una montaña. No es posible que se sienta mejor.