Construimos means "we built" or "we construct". It's the past tense (or present tense, depending on context) of the verb construir (to build).
In this song, Diego Torres sings, "La vida que de a poco juntos construimos" (The life that little by little we built together). It's a poignant word that evokes the shared history and effort put into a relationship, highlighting the deep connection and the pain of being apart from that shared life.
Diego Torres wrote this about missing someone while stuck on the road, and he keeps it in ordinary details instead of big declarations. He opens mid-routine: "De lejos otra vez" ("From afar again"), "Tomándome el café" ("Drinking my coffee"), "Contando días sin volver" ("Counting days without coming back"). The travel itself has worn him down too, always "A dar vueltas por el mundo" ("To travel the world") and having to "Y amanecer en un hotel" ("And wake up in a hotel").
The chorus names exactly what's missing rather than describing a feeling: "No ver tus ojos que me dicen como es" ("Not seeing your eyes that tell me how it is"), and mornings that are "Es más difícil despertar sin ti conmigo" ("It's harder to wake up without you with me"). By the last verse the city goes dark and he's alone in his room, unable to sleep, but he keeps ending on "Pero ya falta menos" ("But it won't be long now") like he's talking himself through the wait as much as her.