Word size
The natural data width a processor works with — how many bits its registers, ALU, and pointers typically handle in one go. "64-bit" means a word size of 64 bits. Among other things, it determines how much memory the CPU can directly address.
What it governs: the word size sets the size of the general-purpose registers, how wide integer operations the ALU does in one operation, and — most importantly historically — the width of memory addresses (pointers). A 32-bit processor can address 2³² bytes = 4 GB of memory (the infamous limit that forced the 64-bit transition when computers started having more RAM). A 64-bit processor addresses 2⁶⁴ (theoretically 16 exabytes; in practice limited but enormous) and has wider registers. The transition from 32 to 64 bits (x86-64, mid-2000s) was a big deal precisely because of the 4 GB ceiling. Note: the word size isn't everything — a 64-bit CPU can have wider data units (SIMD registers of 256/512 bits) for specific operations. A fundamental processor property. Related to ISA and ALU.