When a character (or creature) is hit, the amount of damage is deducted from his hit points. When hit points reach 0, the character is unconscious. The character actually dies if he reaches negative hit points equal to his level. In other words, a fifth level character only actually dies at -5 hit points.
In addition to the various magical means of restoring hit points, a character recovers 1 hit point per day that he takes uninterrupted rest. Four weeks of rest will return a character to full hit points regardless of how many hit points the character lost.