In this sentence, de is the plural form of the indefinite article. It means that some little girls read books.

Usually the plural indefinite article is des. However it becomes de in two cases:

• When the noun group is a direct object of a verb in a negative sentence.

  Le chat mange des souris.
  Le chat ne mange pas de souris. [direct object → de]

  Les chats sont des souris.
  Les chats ne sont pas des souris. [attribut du sujet, i.e. complement to a copula → des]

• Sometimes when there is an adjective before the noun. The article is always des when the adjective and the noun form a set phrase, but it is de in careful speech otherwise. I don’t think des is ever incorrect in this case.

  des beaux yeux or de beaux yeux
  des petites filles or de petites filles

  de petit pains (small loaves of bread)
  des petits pains (specific bread shapes, with regional variations; in some regions, a kind of chocolate croissant)

  de petits enfants (small children)
  des petits-enfants (grandchildren)

The English sentence could also mean that little girls in general (i.e. all or at least many little girls) read books. This meaning would call for a definite article: “Les petites filles lisent des livres”.