Edit by Aerovistae: Regarding the bounty: The current answer is not really sufficiently clear to fully understand the different circumstances in which one might use "ce sont" vs "ils sont / elles sont." There are also other tenses to consider...for instance, should it be "c'etaient"? An answer in English would be preferred for this one.
If for example I want to say "They are children", I would've thought one would use the phrase:
Ils sont des enfants.
... or even:
Ces sont des enfants.
However I think the correct way to say it is:
Ce sont des enfants.
But why is this? Isn't ce to be used with singular nouns, not plural? And why not ils? How can you know where you should use ce in sentences like this, and when to use ils?