Following on from the answer below; how do you then say "I like THE carrots" (i.e. the carrots I have on my plate right now)?
To say, 'I like carrots', you have to use the definite article, les and say -
J'aime les carottes
It sort of indicates in French that you like all the carrots in the world. very strange!
Des is a partitive article meaning 'some' so you might say -
Je voudrais des carottes, s'il vous plait = I'd like some carrots, please
Donnez-moi des carottes = Give me some carrots