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 this case, more hollows) in the Graveyard and gain favor with your Inner Self. Tormenting works just like normal battles; you can get injured (and then healed if you go to the Mausoleum). Once you have 100 favor, you can resurrect back to life.
Note that you may also spend favor on:
- Haunting someone (they lose a turn next game day )= 25 favor
- Blessing your Zanpakutou/armor (your weapon or armor now becomes extremely powerful while you Track Hollows, new buff) = 500 favor
You don't have to resurrect and sometimes you plainly can't; there is still much to do in the Graveyard for entertainment.