Desiertas means "deserted" or "empty." While it's a common word, its use in this romantic context is particularly evocative and interesting.
In the song, the lyric "ya no habrá noches desiertas" (there will no longer be deserted nights) uses desiertas metaphorically. It implies that with the loved one's presence, the singer's nights will no longer be lonely or empty, but filled with companionship and love. This poetic usage makes it stand out.
This song is all about falling in love at lightning speed! It starts with a simple meeting: "Buenas noches, mucho gusto / Eras una chica más" (Good evening, nice to meet you / You were just another girl). But that changes almost instantly. Just five minutes later, he realizes she's "alguien especial" (someone special). The connection is so immediate that even without talking or touching, "algo dentro se encendió" (something inside lit up). It's a perfect description of that love-at-first-sight feeling where time just stops.
The whole song is basically a direct and heartfelt plea for this person to become a permanent part of his life. He's not playing it cool at all. He lays it all out there, begging her, "Entra en mi vida / Te abro la puerta" (Come into my life / I open the door for you). He believes she's the one who can end his loneliness, promising that in her arms, "ya no habrá noches desiertas" (there will be no more lonely nights). It's a super romantic and intense declaration that goes from just missing her to desperately needing her.