How does a New Game + differ from a standard New Game

There are three combat bonus "types": 1-Turn Victor, Unscathed, and Sweeper. 1-Turn Victor boosts the amount of EXP you get from the battle, Unscathed increases the number of JP (Job Points) you get, and Sweeper boosts how much money you receive.

Each of these bonuses come in three gradations: normal, Ace, and Hero. These grades are earned after 1, 5, and 10 battles in a row respectively. The amount of extra points that each combat bonus gives depends on what monsters you are fighting as they are percent increases, rather than flat increases. Normal grants a 10% increase, Ace is 20%, and Hero earns you 50% more.

You can print them out from here:

Bravely Default AR Cards

They are effectively like QR codes that the 3DS can understand. The 3DS will turn on your front facing cameras to show you what is behind your 3DS and superimpose a 3D model where you placed the card. You can also move your 3DS around and get a different perspective of the 3D model.

AR stands for "Augmented Reality"

Side note, I think the game restricts the view angle you can get on the models because:

I can't see up any of the costume's skirts.