Empañando comes from the verb empañar, which literally means 'to fog up' or 'to mist over', like a mirror or window. However, it's often used metaphorically to mean 'to tarnish', 'to cloud', or 'to spoil'.
In this song, Ariel Camacho uses it to describe how something is negatively affecting their relationship: "Hay algo que esta empañando nuestras vidas" (There's something that is clouding our lives). It's a powerful and evocative word that beautifully captures the idea of a hidden issue dimming the brightness of their love.
This song is one big, urgent plea for a conversation. The singer feels something is deeply wrong in his relationship and he's desperate to talk it out, asking his partner, "que platiquemos un segundo solamente" (that we talk for just a second). He's noticed the little things, like how it's been a while since she's said she loves him, pointing out, "a ti ese detalle jamás se te pasaba" (you never used to miss that detail). He can feel the distance between them, saying "eso lo siento aquí en la piel" (I feel it in my skin).
But the most intense part is his attempt to reassure her. He promises he'll never leave, but then adds this incredibly complicated line: "aunque ella haya sido siempre / Lo más sagrado que hay en mí" (even though she has always been / the most sacred thing in me). Who is "ella" (she)? Another woman? His music? It's a strange and almost self-sabotaging way to comfort someone, revealing a deep conflict inside him even as he tries to fix the one with his partner.