It's a common phrase used when ordering a drink or describing a dish that includes milk. For example:
* "Un café avec du lait, s'il vous plaît" (A coffee with milk, please)
* "La soupe est servie avec du lait" (The soup is served with milk)
The phrase literally translates to "with of the milk," but "du" is used in this context to signify "some" or "a bit" of milk.