The sentence is decomposed in the song.
The complete sentence is : Comment expliquer qu'un inconnu finisse toutes vos phrases?
The sentence should be said completely by Hans but is finished by Anna who must be this stranger who ends all the Hans' sentences.
The translation should be "How to explain that a stranger ends all your sentences?" "finisse" is a subjunctive form.
Hans : Comment expliquer
Anna : Quoi?
Hans : Qu'un inconnu finisse
Anna :Toutes vos phrases
Hans : C'est ce que j'allais vous dire!
Anna : Je ne connais personne