To enter the Battle square you must first go to the title manager and get the title and complete which ever title corresponds to the proper area you want to enter.
Players can then enter the battle-square through the ( battle-square supervisor) located in each beginner city.
There are various items that drop from the mobs in battle square as well as items you gain from winning or losing in a PvP match.
what drops and where
Summoning Scroll: floor 1,2,3,4,5,6 bosses
authority of looser: Losing a PvP battle or the lvl 80 boss
Carving of Courage: from failed refine on lvl 4 stones
Medal of Honor: Floors lvl 3,4,5 bosses
Orb of Glory: Floors lvl 4,5 bosses
Authority of the Loser: Floor lvl 6 boss
Proof of Winner: winning a PvP battle or lvl 80 boss
Fighter's Ring: floor 1/2
Required level: 20
Class: All
Bound Item
Attack Rating +12
Damage +10
Attack Speed +10%
4% chance when hit to convert 10% of damage taken into restored health.
Colosseum Necklace: 2 to 4 slots floor 1/2
required lvl: 20
Class: all
Bound Item
Can be 2 to 4 slot.
ele Attacks +15
ele resistances +5
all stats +15
HP recovery +30/10 secs
Defense +5
Boss monsters which spawn every 2 hours from when they were killed are in the center.
They drop weapons armor and some of the farming items mentioned above , the weapons in battle square have unique stats shown below.

You can use some of the items in various ways and exchange them through the event NPC or the refinery , you can use the battle square potions anywhere except for in heavens hell.
carving of courage = 10k charisma
proof of vengeance= 100% charisma for 5 mins
There is an item called a summoning scroll which you can use only in the battle square which will summon monsters to fight along side of you.They drop from boss mobs.
There are also new combination prayer stones that have the effect of 2 different prayer stones in one , you can make these through the refinery if you have the items necessary from the battle square.
To make a combination prayer lvl 1 you actually need:
Piece of Sealed Prayer Stone x 1
Battle Square Spell Scroll x 1
Proof of Winner x 3
Some additional information on drops inside the battle square are that uniques and CF realm drop as well from the mobs.
If I have missed anything let me know and I will change it.