The term 32-bit computer (or 8-bit or 16-bit) refers to the power of the central processing unit (CPU), which is the chip that runs the computer. A CPU that can process 8 bits of information at a time (the minimum configuration for a computer) is called an 8-bit computer. If the CPU can process 16 bits at a time, it is a 16-bit computer, and the same for 32-bit.
But you know what? Even though the CPU can internally process 16 or 32 bits at a time, it doesn't mean the rest of the computer can use that big of a chunk of information. After the data gets processed, it has to get on a bus and be sent to the rest of the computer. Many computers with 16-bit processors (cpus) have an external data bus that is only 8 bits wide, so essentially it doesn't matter whether the CPU is 16 bits or not-only 8 bits can get used at a time anyway. (Yes, you can think of the bus as a little thing with wheels that carts information around to where it needs to go.) The same is true for computers advertised as 32-bit machines; on some computers the external data bus is only 16 bits wide. Nowadays most computers are made with data buses to match the processor.