Death occurs when you run out of health.
When you are dead, you may still move the camera around your resting place, and even pick up items within reach. Furthermore, if you gain a level while dead (for example, in multiplayer an ally finishes off an enemy you were fighting and the XP is enough for a new level) you are returned to life at full health. Thus, there are certain tactics to choosing when to immediately respawn and when to stick around.
If you die, you may choose to re-spawn at the second nearest Respawn Point.