Embriagué comes from the verb embriagar, meaning "to intoxicate" or "to get drunk." While it can refer to literal intoxication, it's often used metaphorically.
In this song, the singer uses it to express how he "intoxicated" or drowned his sorrows and feelings: "Embriagué las penas de mis sentimientos" (I intoxicated the sorrows of my feelings). This powerful imagery conveys a deep emotional state of trying to numb pain, making it a compelling and memorable word.
Banda MS de Sergio Lizárraga brings us a relatable tale of heartbreak and confusion in "Increíble." Our narrator is clearly going through it, sending a message that goes unanswered and wondering, "Será que no quiere seguir a mi lado" [Could it be that she doesn't want to be by my side anymore?].
It seems his ex has moved on, with rumors of a new, wealthy boyfriend who's replaced his kisses with fancy cars. He feels blamed for the breakup, seeing it as an excuse to end things. He's been drowning his sorrows, admitting, "Embriague las penas de mis sentimientos" [I intoxicated the sorrows of my feelings], and found it impossible to tolerate the disrespect. He's also realized that he might have just been a "pasatiempo" [pastime] for her, and the whole relationship was a confusing puzzle with a missing piece that finally helped him see the truth. It's a raw look at the pain of realizing you've been played.