If you get podkilled, your character's original body dies, but your character's mind is transferred to your clone, and you resume the game with the cloned body.
Will I Lose Skills or Attributes if I Get Killed?
You will not lose skills if your character gets killed, unless you were piloting a Strategic Cruiser. The Rhea expansion, released on December 9, 2014, removed the loss of skillpoints when your character gets killed.
Your clone will have the same attributes that you had when killed, but any implants that your character had will be destroyed if your character is podkilled.
How do I get a clone, or upgrade the clone I have?
As of the Rhea expansion, there are no longer any upgrade levels for clones. You automatically have a clone, which is installed in the station you start in.
You can move your clone to a different station if you wish. To do so, go to any station that has medical facilities, and click the medical facilities button (it is in the station information window.) You will see a window that has a couple of tabs: one for clones, and one for jump clones. Jump clones are not within the scope of this article. In the clone tab, you can choose to move your clone to the current station if it is not there already. The tab will show you information about your current clone, including the station where it is installed. That station is where you will wake up if your character gets killed.
What happens in the game world when a character gets killed?
Your character can only be killed via podkilling. A pod is a metallic egg developed by the Jovians that is (presumably) filled with goo and can warp and use jump gates. If the pod is breached, a device in the pod takes a "snapshot" of your character's mind while another device injects your character with a poison that kills the character instantly. Your character's corpse is then left floating in the vacuum of space, where it freezes. Your character's mind is transferred into your clone, which awakens in whichever station you installed it in.