A native born Israeli is known as a sabra, especially if their family has lived in Israel for more than two generations. Really hardcore sabras can trace their roots back to a point where their family was living in Israel pre-1948 (before Israel became a state).
Sabra is literaly a Cactus Pear. The term was extended to definition above since, like native Israelis, the cactus pear is prickly on the outside and sweet on the inside. If you run into enough sabras of either type you'll quickly realise how true this is.
If you're looking for info on Sabra and Shatila you might want to try this link.