an article on french partitive articles here: http://french.about.com/od/grammar/a/articles_4.htm
"Du" is a contraction of "de le". In some cases that translates as "of the" in other cases it translates as "some"
"The hat of the boy" = "le chapeau du garçon"
However in the case of "la fille mange du pain" if we translate "du" as "of the" it makes no sense.
In this case "du" is the partitive article and translates as "some".
In the English sentence the word "some" is optional.
"du" is the masculine partitive article. It is used with masculine uncountable nouns.
We can count apples so we use use "des" with plural apples. "Je mange des pommes".
Milk, bread, soup, meat etc can not be counted.
We use either "du" or "de la" with uncountable nouns. Which we choose depends on gender of the noun.
Checkout link for more information on French partitive articles.