Dejé de existir literally means "I ceased to exist". It's a dramatic and poetic phrase that perfectly captures an overwhelming, all-consuming feeling.
In the song, Luis Fonsi uses this hyperbole to describe the moment he first saw someone. He sings, "Cuando te vi / Todo se fue en un momento y dejé de existir" (When I saw you / Everything went away in a moment and I ceased to exist), expressing that he was so captivated that everything else, including his own sense of self, completely faded away.
Luis Fonsi is laying all his cards on the table in this one! He's spotted someone and he's so completely taken with her that he can't hold back, even though he suspects she might not be looking for love. He just has to tell her how he feels, starting with the very direct plea in the chorus: "Dime que estás sola y que nadie te ve como yo" (Tell me you're alone and that no one sees you like I do). He's convinced that she's the one he's been dreaming of and that she's brought him back to life, even giving him his "voz para cantar" (voice to sing) again.
He makes some pretty big promises to win her over. Fonsi swears that if she takes a chance on him, "Siempre con un beso vas a despertar" (You'll always wake up with a kiss). He even makes the ultimate romantic guarantee: "si te enamoras te juro que me enamoro, de ti" (if you fall in love, I swear I'll fall in love, with you). It's a bold, confident song about finding the person who makes you feel like you have everything you've ever wanted.