An inspector window is a type of computing window

Window (computing)

In computing, a window is a visual area containing some kind of user interface. It usually has a rectangular shape that can overlap with the area of other windows...

 that shows current parameters of a selected object and allows these parameters to be changed on-the-fly. It shows Information in programs, like File Managers, showing File Parameters like File Size and Permissions.

For example, in a vector graphics application

Vector graphics editor

A vector graphics editor is a computer program that allows users to compose and edit vector graphics images interactively on a computer and save them in one of many popular vector graphics formats, such as EPS, PDF, WMF, SVG, or VML....

 the user creates drawings out from elements such as lines, rectangles and circles. When such an element is selected on the page, an inspector will show the current size and absolute position on the page of this element with numbers. The user can then change those numbers to change the size or position of the object on the page.

A inspector window is a type of palette window.