Board Thread:Questions and Answers/@comment-30150700-20161005162327/@comment-4567891-20161005213256

The explanation regarding this is in the very first episode/novel volume. The NerveGear helmet emits intense microwaves that will fry the brain of any player whose HP reaches Zero. There's also no stated guarantee that the revival item will work, but it is speculated that the person could be saved within the ten-second interval before the microwaves activate.

IOW, yes, players really do die in the game. Kirito and Asuna were the sole exceptions because Kayaba wanted to talk to them mostly out of respect for bypassing the laws of his world(Asuna for breaking out of the paralysis through sheer willpower, which he stated to be impossible, and Kirito for managing hold his avatar after losing all of his HP, despite that also being an impossibility, long enough to stab him).