A Neutral Roll is a roll that is performed without touching the control stick. It is done by holding down Z until the action icon reads Attack, then pressing A.
It is unique in that the direction in which Link rolls depends on the the last action that was performed. If you release Z before rolling, you'll always roll forward. If you roll after a backflip, Link will roll sharply to the right at about an 80.2 degree angle off forward. If you sidehop to the left you'll roll at roughly a 40.5 degree angle to the left, and if you sidehop to the right you'll roll to the right with the same angle.
The neutral roll is useful for getting a precise angle for a many tricks.