Asomada comes from the verb asomar, which means to peek out, lean out, or show oneself. It's a descriptive word that paints a picture of someone appearing from a hidden or partially concealed position.
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Estopa's "Mañana Clara" is such a sweet song about being completely swept away by someone you see unexpectedly. The singer wakes up to a beautiful spring morning, feeling happy with "Las flores me decían que era primavera" [The flowers told me it was spring] and "Los pájaros que tengo dentro me cantaban" [The birds I have inside me were singing]. He's just enjoying the day when suddenly, he sees her!
It's like a dream, he says, seeing her on her balcony with her dark hair dancing in the wind. He's so captivated, he feels like he's still dreaming even when he's awake: "De esos que te despiertas y sigues durmiendo" [Of those where you wake up and keep sleeping]. She's become his muse, the one who inspires his melodies, even in his sleep. It's a lovely picture of love at first sight, or at least a powerful moment of infatuation that brightens his whole day.