Maullaré comes from the verb maullar, meaning 'to meow'. It's the future tense, 'I will meow'.
This word is particularly interesting because it directly ties into the song's central metaphor: the singer comparing herself to a 'gata bajo la lluvia' (cat in the rain). After her lover leaves, she declares, 'Seré la gata bajo la lluvia y maullaré por ti' (I will be the cat in the rain and I will meow for you), vividly expressing her sorrow and longing through the image of a lonely, crying cat.
Nuria Fergó and Marina Carmona's "La Gata Bajo La Lluvia" tells the story of a breakup from the perspective of the person being left. It's a really honest and a little bit heartbreaking look at trying to be strong when someone you care about is moving on.
The singer tries to be understanding, saying "Tranquilo, no te voy a molestar" [Calm down, I won't bother you] and acknowledging that "Lo nuestro solo fue casualidad" [What we had was just a coincidence]. But even though she tries to be chill, you can feel the sadness. She imagines herself as "la gata bajo la lluvia" [the cat under the rain], meowing for the person who left. It's a powerful image of feeling exposed and alone, but still holding onto that connection. And there's a blunt, almost desperate line: "Invítame a un café y hazme el amor" [Invite me for a coffee and make love to me] if they ever see each other again. It shows that even with the acceptance, the longing is still very much there.