How does an animal learn what a predator is? A while ago I heard the following anecdote: 


  "On some tropical island, explorers infested the island with rats that
  wrecked the native ecosystem. To get rid of rats, people introduced
  cats that instead of hunting rats killed off the entire island's bird
  population".


The explanation given is that birds could not recognize cats as predators and/or did not have natural predators in the environment. This made me think - is there any part of a bird that on a genetic level knows that some other organism is a predator and is to be avoided?

For animals that live surrounded by predators, for example a house sparrow - how does a bird learn that cats are predators, but squirrels are not? 

An example might help illustrate my question: Let's say someone takes house sparrows from America and breeds them for 3 generations on the same tropical island with no predators - would such 3rd generation sparrow still recognize cats as predators?
To answer your question, you really have to specify what animal your talking about, some animals simply won't live long enough for learning to be an effective mechanism. 

If there are few predators, evolution will favour animals who are less vigilant about checking for potential predators generally, since this costs time (Google search vigilance behavioral ecology).

Do address JeromeJ theory in that comment, teaching is fairly rare in the animal kingdom, even amongst Apes. I don't know any examples of teaching about predator detection, although it is believed that Meerkats teach their young how to kill poisonous scorpions and ants teach each other the location of new sources of food (see http://psychology.wikia.com/wiki/Social_learning_in_animals) 

Rather than explicit teaching, it might be likely that birds socially learn infomation about predators simply from observation, although i'm not sure how often this occurs. A nice little example shows that wild crows learnt to avoid and "mob" specific humans using facial identification http://rspb.royalsocietypublishing.org/content/early/2011/06/20/rspb.2011.0957

I don't know enough to give a more detailed response though!