Madrugada refers to the very early hours of the morning, specifically from midnight until just before sunrise. It's a more poetic and specific term than simply "morning."
In the song, Bustamante sings, "Al llegar la madrugada mi canción desesperada." This sets a romantic and somewhat melancholic tone, suggesting that his desperate song of love emerges in the quiet, reflective hours of the early morning, making the word evocative and memorable.
Have you ever felt a love so powerful you couldn't explain it? That's the heart of this passionate duet. The singers tell their beloved not to ask for a reason for their love, because even they can't fight their own heart. It's a feeling that's a mix of everything: tenderness, fear, and even a little bit of madness.
This song is a direct and desperate declaration. The simple but powerful phrase "Te quiero" (I love you) is repeated over and over, showing the depth of their feeling. They ask for a simple embrace and promise their love will last forever, "hasta el fin"... until the very end.