MUCH OF THIS INFORMATION IS INCORRECT!!! I RESEARCHED THIS AGAIN TO FIND THIS OUT! EXPECT A NEW UPDATE TO CORRECT THE MISTAKES!!!
If you've played the first SF for SNES, you can see that almost everything is made of polygons instead of BG layers and sprites. A game that uses all polygons is a title better suited to an N64 or GCN game, but actually, SF was one of the first home console systems to do this.
One of the things that a system does is execute math computations to determine what you see. The SNES can do around 400 (not sure of the exact number) math computations per second. Star Fox needed over 1000 since it used polygons. To do this, Argonaut, a company Nintendo enlisted, made something called a Super FX chip. This was going to be used to make the SNES able to do what it needed. It'd be in the game itself.
I'm not exactly sure on this, but I think that Miyamoto made some characters and designs for a game where a group of pilots flew around and stuff. The head of the mercenary group was a Fox named Fox (pronounced Fox). The game was going to be just a test for the Super FX chip, but the developers liked it so much that they decided to release it to the public.