Odisea is a direct cognate of the English word "odyssey", referring to a long, adventurous, and challenging journey. It's a very literary and dramatic word that you don't often find in a pop song.
Daddy Yankee uses it to describe the immense difficulty of a long-distance relationship. He sings that this kind of love "termina siendo una odisea" (ends up being an odyssey), a powerful metaphor for the epic struggle and series of challenges the couple must face to stay together.
Daddy Yankee's "La Despedida" is all about a goodbye that feels completely wrong and forced. The whole song is a desperate plea right at the moment of separation. He starts with, "Antes que te vayas dame un beso" (Before you go, give me a kiss), immediately setting up this painful final moment. He knows his life won't be the same and asks, "¿Cómo te voy a olvidar?" (How am I going to forget you?). It's a classic head-versus-heart situation. His lover apparently told him love could change destiny, and he's holding onto that, begging them to stay.
He totally rejects the idea that long-distance relationships work, calling them an "odisea" (odyssey) that he can't stand. While his brain might be telling him one thing, he says, "Pero mi corazón va ganando en esta pelea" (But my heart is winning this fight). He even has a conversation with the man in the mirror, who gives him the old advice: if you love something, set it free. But even with that wisdom, the feeling is one of intense, unending waiting. He declares, "Hasta la muerte aquí estaré esperando" (Until death, I'll be here waiting), showing just how deep this farewell cuts.