The Inspector is used to view and edit object properties and also preferences and other settings within Unity.
When you select a GameObject in the Hierarchy or Scene View, the Inspector will show the Properties of all Components and Materials on that object and allow you to edit them. For a custom Script component, the public variables of that script are also shown in the inspector and can be viewed and edited like the properties of Unity’s built-in components. This allows you to set parameters and default values in your scripts easily without modifying the code.
Additionally, the Inspector is used to edit import options for Assets (files containing textures, 3D models, fonts, etc). Some scene and project-wide settings are also viewed in the inspector, the Settings Managers being the main example.
This section of the manual explains the various things the inspector can do and how you can make use of them.