A claim is 'notable' when a significant number of people believe it is true.
Claims of the kind "I once heard" or "my friend told me" are not notable if your friend is the only one actually believing the claim.
Naturally, a notable claim will have many mentions doing a quick Google search. When Google does not seem to return examples of it, we need to demonstrate notability.
The main way of demonstrating notability is showing the claim being mentioned in the media. Examples include: books, newspapers, mainstream television, or widely-known web-sites including major blogs and Wikipedia. Claims put forward by a celebrity are also automatically considered notable. The idea here is that once a large number of people are exposed to the claim, it is of general interest to validate the claim and either confirm or refute it.
Alternatively, many references to individual people writing about the claim should be enough to demonstrate notability.
Sometimes people say stuff they don't mean to be taken as a claim; e.g. as comedy or in fiction. The claim is only notable if people believe it to be true, or at the very least, if it is clear that the author of the statement intended people to believe it as true (in the real world).