Emigrante means "emigrant," someone who leaves their home country to live in a new one.
This song uses the word in a stunningly creative metaphor: "Quiero ser una emigrante de tu boca delirante" (I want to be an emigrant from your delirious mouth). The singer isn't talking about travel; she wants to 'live' in her lover's words and kisses, making their mouth her new home. It's a powerful and unique way to express an all-consuming desire for intimacy.
Spanish singer Amaia Montero is not holding back any cards here; she wants to be everything to this person, right down to the grammar itself. She sings that she wants to be el verbo 'puedo' ("the verb 'I can'") and una palabra serena y clara ("a calm and clear word"). The Spanish idiom andarme sin rodeos means to stop beating around the bush, and she takes that quite literally when she bluntly admits that one afternoon she simply started dying of love: confesarte que una tarde empecé a morir por ti ("confess to you that one afternoon I started dying for you"). It is dramatic, sweet, and totally head-over-heels.
The real warmth shows up in the chorus when she says she wants to sleep a la verita tuya ("right by your side"). That tiny word verita comes from vera (edge or side), and adding the diminutive -ita makes it sound extra close, cozy, and affectionate, like snuggling in tight. Then she imagines strolling along the coast, amarradita siempre a tu cintura ("tied snug to your waist forever"), reassuring her lover that this crazy romance cannot simply end just because a few doubts creep into their head (por mucho que te entren las dudas).