Madrugada is a special Spanish word with no single English equivalent. It refers to the time between midnight and sunrise, often called the 'wee hours' or 'early morning'.
In the song, the singer nostalgically remembers receiving messages 'en la madrugada', which paints a vivid picture of late-night conversations and the intimate, quiet moments of a past relationship. It's a poetic word that perfectly captures that specific, often memorable, time of night.
This song is all about that weird, complicated feeling after a breakup when the pain starts to fade. The singer is ready to move on, saying, "Que ya quiero bailar y gritar / Que ya no duele igual" (I want to dance and scream / It doesn't hurt the same anymore). The story with this person is completely over, like a book with nothing left to write.
But here's the twist: instead of being bitter, he's actually thankful. He sings that despite all the hurt, the experience made him "más humano" (more human), and he's grateful for it every day. He still looks back on old photos and late-night messages, and admits that the memories, both good and bad, can still get to him. He knows they can't get back together, because trying to love this person now just ruins his peace of mind. It's a song about accepting the past, appreciating the lessons it taught you, and finally being ready to let go.