The partitive article is used in both French and English to talk about quantities that can't really be counted, and translates to some or any. It can be a little hard to grasp for English speakers because we frequently leave it out of our sentences:
For breakfast we have (some) cereal, (some) milk, (some) fruit and (some) orange juice, but we don't have (any) coffee.
In French the partitive article changes depending on whether what you're talking about is masculine, feminine or plural. For instance:
When the sentence is turned into the negative, des, du, de la or de l' (before a vowel) turn into de.