New Game Plus, commonly abbreviated as NG+, is a gameplay mechanic in Dark Souls III. It is a new adventure presented to the player after having completed the game, characterized for having a higher difficulty level and adding a few new items for them to collect (these mainly being higher versions of many rings).
Upon defeating the Soul of Cinder and completing the game, the player will be offered to enter New Game+ immediately. If declined, they will arrive back at Firelink Shrine and will be free to continue exploring the game as normal. New Game+ can then be entered at any time from Firelink Shrine's bonfire.
The process repeats each time the player completes a game cycle, with each new adventure being harder than the last. This continues on until reaching New Game+ 7, which is the hardest mode the game has to offer. Further game cycles can be done, but difficulty will no longer increase.
The story and events in New Game+ are identical to New Game. The player keeps all non-story based acquired weapons, armor, items, and rings; and retains their level, stats, and covenant standings. The primary differences are an increase in game difficulty, in the form of more powerful enemies and a greater reward in souls for their defeat.
Bosses will still drop their specific souls when killed, allowing the player to transpose items they otherwise neglected. This in turn allows one to obtain the Twin Princes' Greatsword without being given items from another player.
The player character's Hollowing stat will be unaffected by starting NG+.
More powerful versions of certain rings can be found throughout Lothric on New Game+. Further additions may be found on the third cycle, New Game++. After this, the only changes are to difficulty and soul rewards.
It should be noted that certain rings have even stronger versions in The Ringed City DLC, which can be obtained without the use of New Game+.