It would be difficult to pinpoint one specific catch-all definition for children's literature, other than to say that it is a term used typically in discussing books written for and enjoyed by those who are under the age of 12 or so. Recently there have been attempts to classify children's books into a set of six categories: picture books, traditional literature, fiction, non fiction, historical biography and poetry.
While its hard to nail down the first children's story, we can be certain that stories for kids have existed as long as there have been stories to tell. Many of these stories, even in modern times, are merely adult stories that have been rearranged and rewritten for the younger set. This can be due to themes inappropriate to children or simply to make the story more exciting and accessible to young minds. Many experts in the field point to Komensky's "Orbis Pictus" as one of the earliest examples of a children's book published on a wide-scale basis. Children's literature also owes a great debt to Aesop and the Brothers Grimm for their fables and fairy tales, which were written specifically for children and quickly attained a mass audience.
If there is one thing of which we can be certain, it is that children enjoy their literature with a side order of illustration. Kids are very visual creatures, and can find themselves bored with characters and situations that too closely resemble their everyday lives. This is why the illustrations in children's literature are often of a fantastical nature, even if the subject matter is (on a surface level) not. Bright colors, animated characters -- these are what speak to children. Children are fascinated by pageantry and by creatures and events that are exaggerated and larger than life. If you need proof of this, see only how many kids are in love with the concept of dinosaurs, and how many girls love the idea of a princess in a magical kingdom.
When speaking of the tradition of children's literature, one can find many of the staples of psychology that have lived on into modern times. There are a number of common facets to these traditional tales. Unknown authorship is one of them, though this is obviously less of a factor of psychology as a tenant of this information being lost to time. Anthropomorphism is another common trait, with animals behaving like people. One example of this is the Little Red Riding Hood story, where the wolf can easily disguise itself as the heroine's grandmother by putting on her clothing and speaking in a grandmotherly voice. In modern times we often see children's books become series, with sometimes endless sequels. This taps into the psychology of familiarity which many children appreciate. Children are often resistant to change, and these series grow more popular as a result.
Studies have shown that children are vastly improved by an early interest in reading. Reading from an early age helps the child's imagination flourish, gives them a greater understanding and grasp of language, makes them better writers and spellers, and gives them a kick-start in school. Recently it has also come to light that the reading of books can improve a child's attention span, something that has come under assault in this modern world of video games, iPods and television.