The Scripts window is the user interface for any Python scripts that are running. Python scripts extend the functionality of Blender and provide useful tools and utilities. Python scripts are written in a high-level language and interpreted at run-time. Using scripts avoids the problems with having to install a new version of Blender to get new features; sometimes those features can be written as a script and simply saved on your computer.
Because scripts can do many different things, each has its own use for the Scripts Window. The fields it contains, and how you use it, are documented with the Script. For more information about what this window contains and how to use it, please refer to the documentation about the script that is being run.