Some tools allow a finer-grained type of selection, so that they can work on a part of a selected object rather than the entire object. This selected part of a selected object is then called the subselection.
One example is the Text tool. You can select an entire text object, but then you can select a fragment of text inside that text object by pressing 
and an arrow key or by dragging the mouse just like you do in a text editor (15.1.1 Selecting). That selected part of the text is the text subselection.
Another example is the Gradient tool. A gradient can have many stops (10.5 Multistage Gradients), and the tool can select one or more of these stops at a time. Naturally, gradient stops are only visible for selected objects, so if you select one stop, you’re creating a subselection within the regular object selection.
When you change subselections, many things in Inkscape behave the same as when you change selections. Perhaps most importantly, the selected style indicator in the status bar (8.1 Style Fundamentals) displays the style of the subselection—that is, the style of the selected text fragment and not the entire text, or the style of the selected gradient stop and not the entire object. Also, any style setting commands (such as clicking a color on the palette, or pasting a style by pressing 
) will apply to the subselection if it is present. In other words, subselection allows you to deal with parts of your objects almost as though they are separate objects in their own right.