Z-Buffer isn't Nintendo marketing, though. It refers to the depth axis in a coord system.
No, it was a hardware feature not present in the Saturn or PS1 that made making games in 3D environments much easier.
http://shmuplations.com/mario64/
Yajima: The N64 hardware has something called a Z-Buffer, and thanks to that, we were able to design the terrain and visuals however we wanted. It gave us, as designers, a chance to play around with Mario in a diorama world, in a very free way. We could do a lot of experimenting—like, we'd make a ghost house course, and then drop Mario in there and see how it felt to move him around there. It was very fun.
—I know it's a bit off-topic, but could you explain what the Z-buffer does?
Tanimoto: To explain it simply, when using it for 3D CG, it helps visually distinguish between foreground and background objects. If you have Mario and an enemy, and they move in front of or behind each other, the Z-buffer is what does the calculations and allows them to appear at the correct distances, with no weird flickering or overlapping.
Edit: also, this thread is great. I honestly never gave the N64 logo that much thought beyond being a cool 3 dimensional N.