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.
In "Me EnRD," American-Dominican bachata star Prince Royce tells a story about a vacation fling that accidentally turned serious. He flies in planning to be a player and break hearts—"Listo para romper corazones" [Ready to break hearts]—while hanging out on the malecón (the seafront boardwalk). He drops his location, grabs a cold Presidente (the classic Dominican beer brand), and starts talking to someone new. Neither person wanted anything serious, but after too many drinks, dancing, and kissing by the water, his whole plan backfires. He wakes up wrapped around this person, totally smitten and ready to write love songs instead.
The genius of the track sits right inside the title's clever wordplay. Royce sings "Y me enredé en RD" [And I got tangled up in the Dominican Republic]. In Spanish, RD stands for República Dominicana, and when you say it out loud, "en RD" sounds almost identical to the word "enredé" (which means I got tangled up or caught up). So the phrase pulls double duty: it says he got tangled up in a romance, while literally being stuck in the D.R. It is a smooth, funny look at how a single night out can completely wreck your best intentions to stay single.