Apoderas comes from the verb "apoderarse," meaning "to take possession of" or "to seize control." It's a strong and evocative verb that goes beyond simple influence, suggesting a complete, almost unavoidable takeover.
In the song, the line "Y no miento, te apoderas de mi pensamiento" ("And I don't lie, you take over my thoughts") shows how completely this person occupies the singer's mind, leaving no room for anything else.
Have you ever been completely smitten with someone who just doesn't seem to notice you? That's exactly what Alkilados is singing about in "Me Ignoras" [You Ignore Me]. Our singer is head-over-heels, confessing, "con mirarte, mas me enamoras" [with looking at you, I fall more in love]. He tries everything to get her attention, even just to talk to her, but she keeps ignoring him.
He's pretty obsessed, admitting, "te apoderas de mi pensamiento" [you take over my thoughts] and feels like "un cero a la izquierda" [a zero to the left], completely overlooked. Despite being constantly rejected, he's persistent, saying, "Tu siempre me rechazas, pero yo insisto" [You always reject me, but I insist]. He even compares his unwavering affection to Manu Chao's famous song, repeating "me gustas tu" [I like you] because he just can't get enough of her, even though she keeps giving him the cold shoulder.