The partitive articles — du (masculine), de la (feminine), and de l' (before a vowel) — express an unspecified quantity of something not normally counted: du pain (some bread), de la confiture (some jam), de l'eau (some water). English often omits this idea entirely ("I'd like bread"), where French cannot: je voudrais du pain.
As with the indefinite article, the partitive collapses to a bare de after a negation: je bois du café becomes je ne bois pas de café. The same happens after most expressions of quantity (beaucoup de, un peu de, trop de) — beaucoup de café, not beaucoup du café.