It would be useful to consult a book, unless someone explains it better here.
EDIT: I missed at least one point, partitive is not only used for uncountables, but also to indicate a part of a set of countable objects, as this article suggests:
http://www.fl.ulaval.ca/fgg/articles/pr ... /art_1.htm
In the sentences of the first group (examples 21-24) the accusative case on the object denotes a whole, and the genitive case indicates a part. The nouns capable of signalling the distinction in Polish by means of the two cases are uncountable mass nouns (such as cukier= sugar) and countable inanimate nouns in the plural (such as jabtka = apples). Cf. :
21. a. Kupilem cukier. b. Kupilem cukru.
I've bought (the)sugar-Acc. I've bought some sugar-Gen.
22. a. Zjadlem zupe. b. Zjadlem zupy.
I've eaten the soup-Acc. I've eaten some soup-Gen.
23. a. Kupitem jablka. b. Kupilem jablek.
I've bought (the)apples-Acc. I've bought some apples-Gen
24. a. Przynioslam jajka. b. Przynioslam jajek.
I've brought (the)eggs-Acc. I've brought some eggs-Gen.