Both "The Stolen Child" and "The Lake Isle of Innisfree" offer a contrast between the mundane, everyday world which we all inhabit and another, much happier natural world in which there is peace, joy, and contentment. A theme common to both poems is that nature is alive whereas the city is dead, and that nature is enchanted whereas the city has long since been thoroughly disenchanted.
In "The Stolen Child" Yeats delves deeply into ancient Celtic mythology to evoke a dreamy, natural landscape where the child may find repose from a world of suffering. Yeats isn't a nature poet; he isn't simply presenting us with a vision of the raw beauty of the natural world. Instead, he offers us a picture of the Irish countryside as a mythical place infused with spirits, fairies, and all manner of strange, ethereal beings. This is what gives life to nature, what forms its beating heart, and makes it the ideal haven for the little child from which to escape the myriad sufferings of a deadening urban existence.