Extenders are components that add, and manage for, properties to other components.
Some extender are not even a separate component. For example, the TableLayoutPanel, FlexLayoutPanel and FlowLayoutPanel are all extenders and add properties to their children. This feature is extremely powerful in a web system, when you drop a control inside a FlexLayoutPanel, that control "gains" new properties such as FillWeight, AlignX, AlignY, etc. These are properties that make sense only when the target control is inside a FlexLayoutPanel.
Return true if the extender wants to extend the target object. There isn't anything more to it and there Microsoft documentation and examples are quite exhaustive.