What is Children's Literature? History, Themes, and Examples.

This is a very tricky subject, because like any other genre of literature, children's literature tends to be vast and fragmented. There are certain classics that are difficult to ignore: more recently the Harry Potter Series, or before that The Chronicles of Narnia, The Hobbit, or the works of Roald Dahl (not to mention the wide range of books and literature that would not be classified as fantasy). To borrow the imagery of Lewis Carrol, we're really falling down a rabbit hole here.
I'm not quite sure how much help anyone can be. We can go back into the nineteenth century and talk about how traditional folk tales were refashioned as children's stories, through the works of Charles Perrault and the Brothers Grimm (and those folk tales, for all that they we label them as children's literature, never lost that earlier sense of menace... consider what happened to Cinderella's step-sisters, just for one example).
And I suppose that would be the main thing I'd suggest keeping in mind: for all that we might dismiss children's literature as somehow "for children", it really is, in its own way, a lot more nuanced and thematically richer than we often give it credit for. Alice's Adventures in Wonderland is loaded with logic games and thought puzzles; Narnia is at its core a theological thought experiment masquerading as a fantasy world; fairy tales tend to be drawn directly from the fears and anxieties of the pre-modern world; and this is to say nothing about the darkness in a work like Coraline or the cruelty you can sometimes see present in the works of Hans Christian Andersen. But again, we can only deal with generalities here, as this topic can really support an entire book on its own merits.