Ahogaban comes from the verb ahogar, meaning "to drown." It's a vivid and somewhat dramatic word that stands out in the lyrics.
In the song, Daniela Spalla uses it metaphorically to describe how time passed quickly and intensely when she was with her lover: "Se nos ahogaban las horas en lo profundo de tu sofá" (Our hours were drowning in the depths of your sofa). This imagery suggests that their time together was so consuming and deep that the hours simply melted away, making it a memorable and poetic choice.
Daniela Spalla frames this breakup song as a swap in nouns. She opens promising, "Voy a dedicarte" ("I'm going to dedicate to you") "Una canción de amor" ("A love song") — so you don't think, she adds, "Que lo nuestro solo me dolió" ("That what we had only hurt me"). A verse later the “canción de amor” becomes "Una canción decente" ("A decent song"), something she says she held back before "Por miedo de arruinarlo y perderte" ("For fear of ruining it and losing you").
The chorus reaches for flood imagery to describe how big the relationship felt: "Fuimos más grandes que el mar" ("We were bigger than the sea"), "Inundamos toda la ciudad" ("We flooded the whole city"), until "Se nos ahogaban las horas" ("Our hours drowned") "En lo profundo de tu sofá" ("in the depths of your sofa"). By the outro she isn't asking for him back — just warning that the song will catch up with him: "Vas a repetirla cuando menos te lo esperes" ("You're going to repeat it when you least expect it").