Entregarle comes from the verb entregar, meaning "to hand over" or "to give". While dar is a common verb for "to give", entregar often implies a more formal or complete act of giving, sometimes even surrendering something.
In this song, the singer uses entregarle in the phrase "Ahora me toca entregarle las llaves de mi corazón a alguien más" (Now it's my turn to hand over the keys to my heart to someone else). This metaphorical use is quite poetic and impactful, signifying a complete surrender of his heart after a past heartbreak, making it a memorable and emotionally charged word.
Ulices Chaidez's "Yo Sí" is a heartfelt, yet a little bit sassy, look back at a love that didn't work out. Our singer is laying it all out, making it clear that he was truly invested, saying things like "Yo sí me había enamorado" [I had indeed fallen in love] and "Yo sí lo había dado todo por todo" [I had indeed given my all for everything].
But, unfortunately, that effort wasn't returned. He sings, "Pero no diste lo mismo y se apagó la luz" [But you didn't give the same and the light went out] and "como vi que no correspondiste, se fueron muriendo los momentos felices" [as I saw you didn't reciprocate, the happy moments started dying]. It's a sad realization that the other person was the one who ended it, as he states, "Tú misma fuiste la que le dio fin" [You yourself were the one who put an end to it]. Now, he's ready to move on, declaring, "Ahora me toca entregarle las llaves de mi corazón a alguien más" [Now it's my turn to hand over the keys to my heart to someone else]. He's making sure there's no doubt about his past feelings, even if it's all in the past now.