What exactly makes some fish "Sushi Grade"?
"Sushi grade" means that it is safe to prepare and eat raw. In order to do that, it must be frozen to kill any parasites. That means it either has to be:
There aren't any official regulations about the fish itself or its quality, and most sushi/sashimi distributors have much more stringent rules of their own beyond the freezing guarantee.
There is no real definition of 'sushi grade' fish. It's purely a marketing term to imply a higher quality piece of fish.
There are some actions that should be done for tuna (really for all fish, but especially for tuna) when they are caught, such as bleeding them immediately, destroying the neural canal, reducing the temperature of the fish immediately, etc.
Here's a blog post on the seven different ways to kill/fillet fish and how those ways affect the taste of the meat.