Madrugadas refers to the very early hours of the morning, specifically before dawn. While it literally means "dawns" or "early mornings," it often carries a connotation of being up late or working through the night.
In this song, the lyric "Ella era famosa por las madrugadas" (She was famous for the early mornings) hints at a lifestyle where the woman was active or known during these late-night/early-morning hours, possibly suggesting a difficult or unconventional life. It's a more evocative and less common word than simply saying "noche" (night).
In this touching live performance, Elvis Martinez tells the story of a chance meeting filled with compassion. The narrator finds a woman crying on a park bench, abandoned and holding a crumpled letter. He learns she is known for working in the early mornings ("famosa por las madrugadas") but instead of judging her, he offers a hug and his coat, telling her not to be sad anymore.
The song is a powerful plea for empathy. The singer believes the woman is a good person at heart who was forced into her life out of necessity, lacking a friend to help her. He encourages her to take his joy, follow her dreams, and leave her past behind, assuring her she won't have to "sell your body anymore." It's a beautiful narrative about seeing the good in people and offering a second chance.