Adormece comes from the verb adormecer, meaning to numb or to lull to sleep. It's a less common word than simply saying 'sleep' and carries a more poetic and evocative nuance.
In the song, iLe sings, "Como cual inyección que te adormece" (Like an injection that numbs you). This imagery beautifully conveys how certain experiences or feelings can subtly dull the senses or make one oblivious, much like a sedative. It's a powerful metaphor that adds depth to the lyrics.
iLe opens by admitting she still can't explain what happened. She gave someone "un lugar" in her life and now she can't find them there anymore, and somewhere along the way the hurt turned physical: "La herida se descose y me supura Pero yo la decoro con pintura" ["The wound comes undone and oozes on me, but I decorate it with paint"].
The chorus is where the trick stops working. "Canto aquí No me hagas caso Que te iré olvidando Paso a paso" ["I sing here, don't pay attention to me, that I'll end up forgetting you, step by step"]. She's narrating her own forgetting out loud, as if saying it slowly enough will make it happen.