You can use triggers to check when something enters that area. A trigger is just a collider in which you set the Is Trigger option. You can create a cube, adjust its position and size (scale) to the area you want to cover, and check the Is Trigger option. Name it "KillArea", then disable the Mesh Renderer : the trigger will become invisible.
Include the OnTriggerEnter function in the player script:

function OnTriggerEnter(col:Collider){

  if (col.name == "KillArea"){ // die only in this trigger!
    // do whatever you want to kill your player:
    // zero health, decrement lives, make him scream, etc.
    // or just write a message to the console to test this trigger:
    print("Arghhh... I'm dead!");
  }

Well, the rest is on you. A good start point is to download the FPS Tutorial Completed and follow the instructions found in FPS_Tutorial_1 to 3.