The Negev (or Negeb) takes its name from the Hebrew neghev, meaning dry. It's located south of Jerusalem and Judea, from which Negev has also taken on the meaning south. Both names are quite appropriate - the Negev is the southernmost area of Israel, and it is most definitely one of the most arid Bible places.
The Negev stretches southward from the mountains and lowlands of Judah where the rolling hills terminate abruptly along the desert. The Dead Sea is located to the east, the Mediterranean Sea is to the west, the Sinai is to the southwest.