32-bit is a collective term for a digital address space that is 32 bits wide.
Every authentic version of Doom and beyond runs on a 32-bit CPU, though some 16-bit operating systems and consoles played a role in serving as a bootloader prior to loading Doom. The most famous example of equipment that enabled 16-bit resources to run software that required 32-bit resources was DOS/4GW which was a memory extender for DOS. To read more about versions of Doom that ran on top of 16-bit hardware and software, see the 16-bit article.
Later on however, the practice of running Doom on top of 16-bit architecture became obsolete since 16-bit architecture itself became obsolete in the years to come.