The Graveyard, oddly enough, is where you go when you get killed and are dead.
The Graveyard is very important. It's where you can resurrect back to life after being killed. To resurrect, you must "torment" souls in the Graveyard and gain favor with Shinigami. Tormenting works just like normal battles, you can get injured (and then healed if you go to the Mausoleum, you may heal those injuries). Once you have 100 favor, you can resurrect back to life.
Note that you may also spend favor on:
- Blessing your weapon/armor (your weapon or armor now becomes extremely powerful in the forest, new buff)= 500 favor
You don't have to be resurrected and sometimes you plainly can't; there is still much to do in the Graveyard for entertainment.