There isn't actually all that much nature in "The Prisoner of Chillon" – after all, the whole thing takes place in a dreary dungeon. The middle brother (the hunter/outdoorsman guy) wastes away and dies in prison because his memories of nature are so strong that he can't stand being in a dungeon. But, for the speaker, memories of the world outside the dungeon actually keep him going. The glimpses the prisoner has of the natural world – the bird that appears at the grate after his youngest brother dies, the view of the lake and mountains he can see from the grate – give him the will to live after everyone dear to him has died.
The mysterious bird that visits the speaker at line 266 represents the power of the natural world to heal the speaker's troubled mind.
The appearance of the bird in "The Prisoner of Chillon" can be viewed as the inevitable influence of Romantic-era nature poetry on Byron.