After specifying search criteria and running the search, you get a list of points as a result. You can move this list by swiping your finger over it. By long press of the point header, you view its detail (position, description, comments and Wikipedia link). By touching the header, the map is moved so that its center is in the point.
All the points on the list are displayed on map. Therefore, you affect the points displayed on map by removing points from list. That is what the checkbox next to the point names are for.
Generally, either you check the points want to have displayed on map, or the points you do NOT want to have displayed on map. So, after selecting the points, Select button comes to action.