32-bit is a term applied to processors, and computer architectures which manipulate the address and data in 32-bit chunks. It is also a term given to a generation of computers where 32-bit processors were the norm.
The range of integer values that can be stored in 32 bits is 0 through 4294967295, or -2147483648 through 2147483647 using two's complement coding. Hence, a 32-bit processor can address 4GB of memory.
The external address and data buses are often wider than 32-bits but both of these are stored and manipulated internally in the processor as 32-bit quantities. For example, the Pentium processor is a 32-bit machine, but the external address bus is 36-bits wide, and the external data bus is 64-bits wide.
Human eye is not capable of seeing more than 32-bit.
See also: 32-bit application, 32-bit era, 16-bit, 16-bit application, 64-bit