Desertar means "to desert" or "to abandon." While it can refer to leaving the military, it's often used metaphorically to describe abandoning a cause, a relationship, or a commitment.
In "Sin Explicaciones," Alfredo Olivas uses desertar to talk about who was the first to give up on the relationship, singing, "Que quede claro que no fui el primero en desertar" (Let it be clear that I wasn't the first to desert). This word adds a strong, almost dramatic tone to the breakup, implying a sense of betrayal or a definitive surrender of the relationship.
"Sin Explicaciones" is Alfredo Olivas asking for a clean break, not a long conversation about it.
He opens by refusing to hear the reasons: if the other person has already made up their mind, he doesn't want the lecture or the runaround, just the truth stated plainly. As the song moves on, he admits he actually made the same decision himself a while ago, without fully knowing how or when it happened. He isn't angry, and he isn't asking to be talked out of it.
What he does ask for is honesty on the way out. He'd rather the two of them call it even than have one side sneak away quietly, and he makes clear he wasn't the first to give up on the relationship. It's a song about ending things with dignity instead of drama.