Sin pagar renta is a clever phrase that literally means "without paying rent". It's the central metaphor of the song and a very modern way to talk about a breakup.
In the song, Xavi describes how the memories of his ex-lover continue to occupy his mind against his will. He sings that they "viven en mi mente sin pagar renta" (live in my mind without paying rent), creating a powerful and relatable image of thoughts that are like unwanted tenants you just can't evict.
Have you ever had a memory of someone that just won't leave your head? That's exactly what Xavi is singing about in this track. He describes a relationship that completely changed him, saying this person "Llenaste el vacío que nadie llenó" (You filled the void that no one else filled) and even altered his whole idea of love. The problem is, he thinks letting them have that much power was his big mistake.
Now that they're gone, he's stuck in a classic battle between his head and his heart. He knows it's over, but his heart "no lo comprende" (doesn't understand). The best line in the whole song is the title phrase: he wishes he could erase the past, but the memories "viven en mi mente sin pagar renta" (live in my mind without paying rent). They're like unwanted roommates he just can't kick out, and he's resigned to it, admitting, "No me queda de otra" (I have no other choice).