Presumas comes from the verb presumir, which means "to boast" or "to show off". It's an interesting word because it carries a slightly playful or even defiant tone.
In the song, Carlos Vives sings, "Para que presumas que fue por tu amor" (So that you can boast that it was because of your love). He's telling his former lover that this final, heartfelt song is for her to brag about, implying that his heartbreak and musical creation are a testament to their powerful, albeit ended, relationship. It's a unique way to express both pain and a touch of pride.
The breakup lands after the album is already finished. Me pediste que te olvide (You asked me to forget you), and then comes the complication: Yo que había grabado un disco / Que lleva tu nombre y lanzaba en diciembre (Me, who had recorded an album that carries your name and was coming out in December). The record is made. The release date is set. The woman it was named for has just asked him to stop calling. What he keeps circling back to is the small humiliation of the admin: Y ahora no sé qué decirle / A todos los amigos que estaban pendientes (And now I don't know what to tell all the friends who were waiting on it).
The ambition in here is funny and very specific. He did not want vague success, he wanted a Grammy Que diga 'Juliana' escrito en el membrete (that says 'Juliana' written on the letterhead), and then En la promoción con Sony / Que está programada por tres continentes (the Sony promo run booked across three continents). By the second verse he has talked himself down: Qué me importa ser famoso / Si me pierdo todo lo que hace la gente (What do I care about being famous if I miss out on everything other people get to do). The chorus is where he lets it go, with better manners than most breakup songs manage: Este es el último disco y aquí me despido, no guardo rencor (This is the last album, and here I say goodbye, I hold no grudge). One last record in her name, sung to the beat of her heart, and then the accordion plays it out for a minute and a half.