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Polygon picker allows you to pick a polygon in any of the views in Layout (regardless of the view mode) and then perform actions based on that selection, such as opening the Surface Editor or the Node Graph editor for the surface used by that polygon.
Advanced options allow you to customise is just the first polygon is selected, or all polygons underneath the mouse cursor.
Additionally, items underneath the mouse cursor may be added to or removed from the current item selection in Layout.
This is a layout tool and can be assigned to a shortcut or a button in the user interface.
As with all tools, it has to be dropped once you're done with it (the easiest way is to press the space bar).
The panel exposing the settings can be opened using the n key any time the tool is active. The settings are stored in the LightWave 3D config directory for the LightWave 3D version you're running.
This open is only available if First Polygon Only is disabled.