[i] John Kerry, a Democratic candidate, made a speech today.
[ii] The Democratic candidate John Kerry made a speech today.
It’s all about semantics. The commas are necessary in [i] to indicate that the noun phrase "a Democratic candidate" is supplemental information, useful perhaps, but not essential in enabling the reader to identify exactly who it was that made a speech today. Noun phrases set off with commas like this are called 'supplementary' (or 'non-restrictive') appositives.
Now consider [ii]. This time the appositive NP "John Kerry" is tightly integrated into the matrix NP; it provides essential information required to identify which Democratic candidate is being referred to. We understand that it was not just one of presumably several Democratic candidates who made a speech today, but specifically John Kerry. Appositives like this are called 'integrated' (or 'restrictive') appositives’.
[iii] The kid, who owns toy cars, is nice.
It’s an unlikely sentence, but nevertheless it is another supplementary construction – this time not an appositive noun phrase, but a relative clause. The writer is saying simply that the kid is nice. Owning toy cars is supplementary information, not essential in identifying which kid is being referred to. The fact that that "the kid" is a definite NP tells us that it is discourse-old, i.e. previously mentioned elsewhere.
If the writer had wanted to say that it is only the kid who has toy cars that is nice, then the commas would have been omitted, as toy car ownership would have been essential information in identifying which kid was being referred to.