In this context, en, just like the English “one” you used, is a nicer way to repeat “the book”.

You could totally say “elle a déjà un livre, mais elle veut un nouveau livre”, which is correct grammatically and very understandable.

However, the repetition is something one would like to avoid, for it is clearly not subtle. That is why, just like other groupes pronominaux can be replaced by le, la or les, you can replace un nouveau livre by en.

In case you are interested by further information about the use of en and its “grammatical properties” (in this context – please note en is a very used word in French and has a lot of meanings and uses for it covers a wide range of roles in the sentence) :

• en is an pronom personnel, it means it goes before the verbe
• en is an invariable pronom personnel : there is not masculine/feminine or singular/plural ! This is rare for a pronom personnel !
• it replaces a complément d’objet direct (if you need help with the French pronouns and compléments d’objet, this can help I guess http://www.frenchtoday.com/blog/understanding-french-pronouns)
• when en is not a pronom personnel, it is a préposition ! You can find more examples about this form here : https://fr.wiktionary.org/wiki/en#Pr.C3.A9position

Hope I could help !