A WLX file is a GIS file created by the MapSource software that comes with the Garmin map products. It contains a Geographic location (in the form of latitude-longitude) in XML format and a world location to a mapping website such as Google Maps or Bing maps. WLX file acts as a shortcut link and opens the stored location in third-party websites at recorded latitude-longitude position.
Another similar file (though not related to GIS) is URL file format that stores the web address and directs users to this URL when opened.
WLX File Format - More Information
WLX files are stored in text file format that can be opened in any text editor to view and update its contents. MapSource is a GIS based software that lets you view maps, waypoints, routes and tracks. You can also transfer this spatial data to or from a Garmin GPS device.
MapSource is no more supported by Garmin and has been replaced by BaseCamp that is available to download for free.