Apoderaron comes from the reflexive verb apoderarse, which means to take possession, seize, or take control of something. It is a wonderfully dramatic word that adds intense emotion to any sentence.
In the song, Rauw Alejandro sings, "Tus ojos color café / Se apoderaron de mí" (Your brown eyes / Took control of me). He uses this powerful verb to describe how completely captivated he is, creating a poetic image of being willingly overpowered by someone's gaze.
Rauw Alejandro's "Tattoo" is a super smooth and flirty Reggaeton track all about being completely captivated by someone. The whole song is basically him listing all the reasons he's obsessed with this person. He's not shy about it at all, saying things like "Estás pa' comerte toda todita" (You're good enough to eat all up) and that he's mesmerized by "esa carita y ese tattoo" (that little face and that tattoo). It's that feeling when you're so into someone that you get flustered just being near them, and he admits "Yo no sé ni qué hacer / Cuando estoy cerca de ti" (I don't even know what to do / When I'm near you).
He's trying to move things beyond just being friends, telling her he's "Muero por un beso de esos que no son de amigos" (Dying for one of those kisses that aren't from friends). The vibe is very much about late-night plans and wanting to spend more time together. He invites her to stay over if the party ends late and makes it clear he wants her and only her, asking her to let him be her "número uno" (number one). It's a straightforward song about attraction and wanting to take a connection to the next level.