Inspector windows are small windows that allow you to change settings for whatever happens to be the currently selected object. They are the ones that have a thinner title bar, they always hover above other windows and they disappear when you change to a different application.

In most applications they contain information and settings about whatever object is selected. As you select different things, the contents of the inspector window will change, so you can always go to the same place to change the properties of that object.

Now you don't want multiple inspectors popping up, containing settings for different objects, because they are designed to keep all the information and properties in one location, so you always know where to find it. However, you might want multiple inspectors that contain different sections of the settings. For example, you might want one inspector for text settings, and one for graphics settings.

In most Apple applications, there is a single inspector with tabs along the top that allow you to change between different groups of settings. If you find yourself constantly jumping between different tabs while you work, there is a simple way to separate each tab out into its own inspector. Simply hold the Option key while clicking on a tab, and another inspector window will appear with the contents of that tab.

Using this, you can arrange the different inspectors around your screen for easier access. For example, in Pages you might want to keep separate Graphic, Text and Table inspectors always open.