The Polygon Selection tool enables you to draw a polygon around UV elements in order to select them. Your first mouse click creates the starting point and subsequent clicks create new corner points. To complete the selection, either click on the starting point or right-clicking.
In the Active Tool manager, if Tolerant is enabled all UV elements that are inside the marquee or intersected by the marquee are selected; If Tolerant is disabled, only the UV elements that are fully enclosed by the marquee are selected.
If Only Select Visible Elements is enabled, you can only select elements which are visible, i.e., not behind other elements. For example, you can select the polygons at the front a sphere but not the polygons at the back.
See Rectangle Selection.