'Des' is not a possessive, in this sentence it is the partitive article. It translates roughly as 'some', e.g. "we are some girls", which sounds odd in English but is grammatically necessary in French. You cannot just say 'nous sommes filles' in French, and if you said 'nous sommes les filles' it would translate as 'we are THE girls'.
"Des" is the plural of "un/une": un livre (a/one book), des livres (books as more than one book). "Des" is required to mean "more than one" with any plural, countable noun.
"Du" and "de la" are partitive articles (partitive = part of a mass); they are used with uncountable nouns.
- Elle mange (no S) du porc (uncountable, masculine)
- Elle boit de la bière (uncountable, feminine)
- Elle prend de l'eau (uncountable, feminine, starting with a vowel sound).