Enredé comes from the verb enredar, which literally means 'to tangle'. It's a fantastic word that can be used both literally, like a rope, and figuratively to mean getting caught up or involved in a complicated situation.
In the song, Prince Royce plays with this word in the title 'Me enRD', which sounds like 'Me enredé' (I got tangled up) while also saying he got involved in the 'RD' (Dominican Republic). He uses it to describe a surprise vacation romance that started with a kiss and became something more, perfectly capturing the feeling of getting unexpectedly swept away.
Have you ever gone on vacation planning to just have fun and maybe be a little bit of a heartbreaker, only to have it all go completely sideways? That's exactly what happens to Prince Royce in this song. He's on vacation in the Dominican Republic, and his plan is simple: "A pasarla bien como se supone / Listo para romper corazones" [To have a good time as you're supposed to / Ready to break hearts]. He's definitely not looking for love.
But then, at a bar on the malecón, he meets someone. They talk, they dance, they share a Presidente beer, and one thing leads to another. The next morning, he wakes up completely surprised: "Y me enredé en RD / Y ahí a tu lado abrazado desperté" [And I got entangled in the DR / And there I woke up, hugging you]. He admits he doesn't remember everything that happened, but he knows one thing for sure: "Sólo sé que tu boca se enredó en la mía / Y me olvidé que enamorarme no quería" [I only know that your mouth got entangled with mine / And I forgot that I didn't want to fall in love]. His simple vacation plan got very complicated, very fast.