Telón literally means 'curtain', specifically the kind found in a theater. It's a word that evokes a sense of drama and finality.
In this song, Jesse & Joy use it metaphorically in the line "Y bajemos el telón" (And let's lower the curtain). This powerfully conveys the idea of bringing an end to their relationship, like the closing of a play, making it a memorable and poignant choice.
This song is about the very end of a relationship, when there’s no point in blaming anyone anymore. The singers know "no hay marcha atrás" [there's no turning back] and are in the middle of the sad, awkward process of splitting up their shared life. They're dividing up their things, from the toaster and the CDs to a fake Picasso painting. It’s all very practical and feels completely final.
But amidst all the heartbreak and packing boxes, they get to the most important question. After deciding who gets the furniture, they ask, "Si tú te vas y yo me voy / ¿Con quién se queda el perro?" [If you leave and I leave / Who does the dog stay with?]. It’s a funny and very real problem that cuts through the sadness. The singer tries to put on a brave face, admitting, "Si no me vez llorar es sólo que mi orgullo no me deja" [If you don't see me cry, it's just my pride that won't let me], but the question about their pet shows the real, everyday things that get torn apart during a breakup.