Increasing the word size reduces the number of instructions the processor must execute in order to perform an operation on variables whose sizes are greater than the length of the word. (For example, consider a case where an 8-bit processor must add two 16-bit integers. The processor must first add the 8 lower-order bits from each integer, then add the 8 higher-order bits, requiring two instructions to complete a single operation. A 16-bit processor would be able to complete the operation with single instruction)
Historically, 4-bit microprocessors were replaced with 8-bit, then 16-bit, then 32-bit microprocessors. This trend generally came to an end with the introduction of 32-bit processors, which has been a standard in general purpose computing for two decades. Only recently, with the advent of x86-64 architectures, have 64-bit processors become commonplace.