"The cats eat fish."
Translation:Les chats mangent du poisson.
"du" is used when there is no specific quantity such as "some" in English. du beurre (some butter), du sel (some salt), du vent (some wind)..
des is used when you can count the subject... des hommes (which is more than one man) des fraises (more than one strawberry), des jours (more than one day).
Those are the endings related to the verb infinitives: I, You, He/She/It, We, You, They. i was taught to remember the endings as "E,Es,E,Ons,Ez,Ent. So if you would go with the I form, speaking about yourself your verb or word should end with e. if you are speaking about You, someone else, you would use ES at the end and so on. Example: "Habiter- to live" -j'habite- (i) -tu habites - (you) -il/elle habite (he/she) -nous habitons (we) -vous habitez (you/plural) -ils/elles habitent (they)
It isn't unclear whether 'poisson' is singular or plural. It's singular because otherwise it would have been 'poissons'. And because 'poisson' is singular 'des' doesn't work, but 'du' does.
However, it is unclear how much fish the cats eat is, and because this is unclear you use the partitive article (du, de l', de la, des). If you want to you can translate the partitive article with 'some':
- Les chats mangent du poisson - The cats (some) eat fish. (The amount of fish is unspecified.)
- Les chats boivent de l'eau - The cats (some) drink water. (The amount of water is unspecified.)
- Les chats mangent de la viande - The cats (some) eat meat. (Idem dito)
Usually these things are singular (eg poisson, eau, viande) but sometimes things that are singular in English are plural in French and then you use 'des':
- Nous mangent des épinards - We eat (some) spinach.
There are some more rules and exceptions and other things you might want to know listed here: http://french.about.com/od/grammar/a/de-vs-du-de-la-des_2.htm
"Some" is not necessary in English, but "du" is required in French, when the noun is uncountable, masculine and starts with a consonant sound.
Also, please read the rest of the thread where explanations and comments have already answered your question a number of times.