Amarrar literally means "to tie up". In this context, it's a popular slang term for being "tied down" in a committed relationship.
Maluma sings, "Era perro y me amarraron," which means "I was a dog (a player) and they tied me up." He's playfully describing how he fell so deeply in love that he left his wild single life behind. It's a colorful and very common expression you'll hear in Latin music and culture.
Colombian star Maluma trades heavy club beats for acoustic warmth in "ADMV", which stands for Amor De Mi Vida ("Love of My Life"). He looks far past the honeymoon phase, imagining what happens when old age sets in: "Cuando los años nos pesen y las piernas no caminen" ("When the years weigh on us and our legs can't walk") and "la piel ya no se estire" ("our skin no longer stretches"). His ultimate wish for when memory fades and only photos remain is simple: "Que se me olvide todo, menos que tú eres mía" ("May I forget everything, except that you are mine").
Even with such heavy romantic promises, he slips in plenty of playful, colloquial Colombian flavor. He jokes about his wild bachelor past ending with the blunt line "Era perro y me amarraron" ("I was a dog and they tied me up"), admitting his heart was happily stolen. He also drops Colombian slang like "parches under", where parche means hanging out or chilling with a crew, showing that his partner fits in everywhere from fancy outings to low-key underground spots.