Windows is the the shorthand name usually referring to Windows 3.11 (or Windows for Workgroups 3.11). It is a graphical shell as well as a thin Operating Environment (not quite an operating system, but close) for applications to share information and interact with certain hardware (like Sound Cards, Printers, Networking (in later versions), Mice etc). While Windows is not a game, the ability to run windows opens up a new library of games that cannot run from the command line.
Windows makes heavy use of system hardware so while it executes, there is still a lot of work to do in making each aspect of it work. The overall status of Windows is that it can work (to a degree) but this level of compatibility varies version to version.
Making it work
To get Windows before 3.0 to run, you must set the DOS version to a pre 5.0 number. Ex: VER SET 4.0
3.0 does not need this, and will run with DOSBox's default setting of 5.0.