um... I guess this is a spoiler so I'll hide it, but not really.
When you beat the game you'll get the credits, then after the credits you'll start over back in your cell at the beginning of the game.
NG+ offers:
Enemies hit harder, can take more damage, and are harder to kill. Even small enemies can put out a lot of damage, but they also give more souls (varies between 2x-5x as many);
You lose all of your embers. craft your weapons before beating the game.
You lose all of your keys except for the Master Key
you lose certain rings that I won't say
you lose a key to the painted world that you find somewhere that I won't say.
the door to darkroot garden closes again
Domhnall of Zena sells you Gwyn's armor, the Great Lord's Set;
You can offer the Soul of Gwyn, Lord of Cinder at the Altar of Sunlight as a rank +1 member of the Warrior of Sunlight covenant to receive the Sunlight Spear miracle;
You lose the repairbox, weapon smithbox, and armor smithbox;
Rite of Kindling is removed; however, kindled bonfires retain their status, so kindle as many bonfires as high as you'd like before starting NG+;
You cannot level up until you get to Firelink Shrine, so try not to lose the souls received from Gwyn, Lord of Cinder before you get there;
Hidden paths and walls are restored - All hidden walls that have been removed in your first playthrough are there again.
Crystal lizard counters increase by +1 each new game, from 0 to 1, 1 to 2 etc. Exterminating them at the end of each game is no longer a necessary chore.
Enemies that carry shields have a much higher poise value,
Overall, enemies have 3x the amount of health, 3x the amount of damage dealt, and 3x the amount of aggression towards the player;