"Death cloning" is the act of instantly teleporting yourself across the galaxy by self-destructing your pod while in open space. You will awaken in whatever station houses your medical clone. You will have lost all of your implants. Don't forget to immediately pay the fee to upgrade your clone to hold your full set of skill points! If you do not, the next time you are podded, you will lose one level off one of your highest level skills and will have to retrain it. This skill loss is permanent.
Why death clone yourself? There are a couple of common reasons.
The most common reason to death clone is because your ship has been destroyed in PvP combat and you believe it not worth the trouble to fly the clone all the way back to one of your home bases. This is a choice most often made with a non-implanted clone, which are quite common in null-sec PvP combat. If your fleet had to travel several dozen jumps before finding the fight in which you lost your ship, and you do not have implants in your PvP clone, then it might be worth the cost to simply reappear back at home rather than taking the time to travel all the way back home (and perhaps get podded on the way back anyway). Time is money, as they say.
Still, there are common ways to use death clones strategically or tactically. As I said in a previous definition, many players have cyno alts that they use to light cynosural fields for the capital ships owned by their main pilots. If this is the case and you previously spread cyno ships across stations where you commonly light cynos, you can immediately death clone your cyno alt's character to one of these stations. To do so, you just dock at the closest medical station, reset your medical clone to this distant station before death cloning. You can often set your medical clone to quite distant locations.
This is even more convenient if your cyno alt is in a corporation with offices spread around the galaxy. You can reset your medical clone to any station where your pilot's corp has an office.
Death cloning is also occasionally done with trade alts, in the same way. In this case, the purpose to death cloning is to determine the prices in the market system jumped to without having to fly all the way there.
In both of these cases, it is advantageous to use clones with 900,000 SP or fewer. These clones pay no medical fees for upgrading their clones to hold all of their skill points since the free clone can hold this many skill points.
Occasionally on Sundays, I will be defining a common EVE term for those who might not have heard it. If you have a suggestion for such a term, please drop it into the comments.