A term describing a computer architecture with an ALU, registers and data bus which handle 64 bits at a time.
64-bit processors were quite common by 1996, e.g. Digital Alpha, versions of Sun SPARC, MIPS, IBM AS/4000. The PowerPC and Intel were expected to move to 64 bits at their next generation - PPC 620 and Intel P7.
Being able to deal with 64-bit binary numbers means the processor can work with signed integers between +-2^32 or unsigned integers between zero and 2^64-1. A 64-bit address bus allows the processor to address 18 million gigabytes as opposed to the mere four gigabytes allowed with 32 bits. In 1996 hard disks could already hold over 4 GB. Floating point calculations can also be more accurate.
A 64-bit OS is needed as well to take advantage of the CPU. In 1996 there were only a few 64-bit operating systems, including OS/400, Digital Unix, Solaris (partialy). A 32-bit OS can run on a 64-bit CPU.