If you think about English for a moment,

there are some nouns which you can count:

one apple, six apples, four score and seven apples

and some which you can't:

ink (you can't say, for instance 'Wow, what a long letter! you
must have used half a dozen inks to write it')

The second, incidentally, is called a mass noun. If you want to describe its quantity you have to use 'some' ('I've got some ink on my shirt'). (For more precision, you can count the containers: 'I used half a dozen bottles of ink to write it', 'I've got half a dozen bottles of ink on my shirt', but you can't count the noun itself.)

In fact, a lot of nouns (especially in English [*note about American English]) can be either countable or uncountable, but their meaning changes slightly. Think of chocolate, for example (yes, please!):

I love chocolates. I eat chocolates every day. (chocolate = countable noun) I love chocolate. I eat chocolate every day. (chocolate = uncountable noun)

The first example refers to the substance itself, in any shape or form. In the second example the meaning has changed and refers to those individual pieces that come in fancy boxes with ribbons and are stuffed with liqueurs and nuts and soft centers and caramel and almonds and nuts and hard centers and liqueurs and nuts and... Mmmmm!

So in French the difference between countable and uncountable nouns is marked by the use of indefinite articles (un, une, des) for countable, and partitive articles (du, de l', de la) for uncountable:

Je mange des chocolats tous les jours. (those individual pieces that come in fancy boxes...)
Je mange du chocolat tous les jours. (the substance, in any shape or form)

FINAL WORLD OF CAUTION