Idilio translates to "idyll" or "love affair." It's a beautiful and somewhat poetic word that evokes a sense of romantic, often idealized, love.
In the song, Jorge Celedón uses it to refer to the romantic relationship that is coming to an end, singing "Aunque nuestro Idilio se termine" (Although our idyll/love affair ends). It adds a touch of wistfulness and a classic romantic feel to the breakup narrative.
This song is a heartfelt and mature goodbye to a lover. The singer, Jorge Celedón, takes a sensible approach to a breakup, deciding not to look for reasons to blame his partner. He admits it was his own fault for trying to force a relationship between two people whose hearts were "not aligned" (corazones que no están alineados).
Instead of anger, the song is filled with well wishes. The chorus repeats the phrase "Que te vaya bien en tu camino" (May you do well on your path), showing a deep sense of care even as the romance ends. He acknowledges they tried "one and a thousand times" but realizes it's better to give up to avoid more pain. It's a beautiful message about letting go with love and wishing the best for someone, even when you have to go your separate ways.