historically, claiming a throne by ancestry was the equivalent of declaring war (or having war declared upon you). Among the more famous claims were the claim of the English throne by William of Normandy and the claim of France's crown by Edward III.
In EU, it should be the means to get the nation recieving the insult to declare war (or at least give them a cassus belli), but apperently it doesnt do that, making it (and the other insults) rather useles. you cant even gain friendship from the enemies of he who you insult.
thanks