What was the advantage of a 64-bit processor in the N64?
The use of "64 bits" was probably as much a marketing term as anything, but not entirely without meaning.  On many machines of that era, any time the display controller spent fetching data from RAM was time the CPU or other chips couldn't access that same RAM.  The less time the display controller spent on RAM access, the more time the RAM would be available for other purposes.  If at a particular display resolution and RAM speed, a 16-bit bus would be 90% consumed by the graphics controller's display-data fetches, other chips would only be allowed to access the bus 10% of the time.  Moving to a 32-bit bus would drop the display controller's overhead by half (to 45%), meaning other devices could access the bus 55% of the time.  Even if the other chips could only perform 16-bit accesses, they'd still see a 5.5x speed improvement.  Pushing the bus to 64 bits would cut the display controller's share in half again (to 22.5%), leaving 77.5% available for other stuff--another 40% improvement.  Not as huge an improvement as going from 16 bits to 32 bits, but significant nonetheless.

Note that if one were using a higher color mode, it's possible that 16-bit bus utilization would have been over 100% (meaning a 16-bit bus simply couldn't handle such a mode), and 32-bit utilization might be over 50%.  Under that sort of scenario, the improvements going from a 32-bit bus to a 64-bit bus would be more significant (again, even if no chips other than the display controller can exploit 64-bit accesses).  Of course, if some other chips (e.g. ones that are designed for copying large chunks of display data) can exploit 64-bit accesses, those chips would receive even further benefit.