The Free On-line Dictionary of Computing (30 December 2018):

32-bit application

    IBM PC software that runs
   in a 32-bit flat address space.

   The term 32-bit application came about because MS-DOS and
   Microsoft Windows were originally written for the Intel
   8088 and 80286 microprocessors.  These are 16 bit
   microprocessors with a segmented address space.  Programs
   with more than 64 kilobytes of code and/or data therefore had
   to switch between segments quite frequently.  As this
   operation is quite time consuming in comparison to other
   machine operations, the application's performance may suffer.
   Furthermore, programming with segments is more involved than
   programming in a flat address space, giving rise to some
   complications in programming languages like "memory models"
   in C and C++.

   The shift from 16-bit software to 32-bit software on IBM PC
   clones became possible with the introduction of the Intel
   80386 microprocessor.  This microprocessor and its successors
   support a segmented address space with 16-bit and 32 bit
   segments (more precisely: segments with 16- or 32-bit address
   offset) or a linear 32-bit address space.  For compatibility
   reasons, however, much of the software is nevertheless written
   in 16-bit models.

   Operating systems like Microsoft Windows or OS/2 provide
   the possibility to run 16-bit (segmented) programs as well as
   32-bit programs.  The former possibility exists for backward
   compatibility and the latter is usually meant to be used for
   new software development.

   See also Win32s.

   (1995-12-11)