The object inspector is a pane that lists settings and options for the selected item (note some options are also available in the context menu that pops up when you right-click on the item as well). When you select an item (i.e. data set, page, table, variable, etc), the object inspector appears on the left side of the screen between the Report/Data Source panes and the work area in Displayr. For Q, the object inspector appears on the right side of the screen when selecting items in your Report.
For example, below, the object inspector shows formatting options for a Visualization. In the example below, there are three tabs: Data, Appearance, Chart, and General. Different outputs have different tabs. The most commonly appearing options in the General and Appearance tab are described below (the other tabs are described in the documentation that describes whatever type of object has been created, such as Visualization Options).
General
Name The Name that appears when an object is shown in the Report tree in Q and Displayr, which is also commonly used in exports.
Reference name The name that the object is referred to when writing R Code. (In Displayr, this is referred to as the Name.)
GUID The reference name used when referring to an object in the underlying code. This can only be used when creating hyperlinks in Displayr.
Appearance
General formatting options such as exporting, layout (units are in pixels), and coloring (for non-visualization items) are available on the appearance menu.