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 instance, if you asked me what I had for breakfast this morning I might say that I had cereal, milk, fruit, and orange juice, but I didn't have coffee. What I really mean is:
For breakfast I had [some] cereal, [some] milk, [some] fruit and [some] orange juice, but I didn't have [any] coffee.
In French, the partitive article isn't left out. It also 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.