The term is most commonly used when discussing military actions, notably during the Battle of the Atlantic (both of them) when the German Kriegsmarine attempted to blockade the UK with U-boats operating in this area. Since almost all shipping would pass through this area, it was an excellent hunting ground and had to be heavily defended. During WWII the task was so important that it had its own commander, and the HQ was moved to Liverpool to be closer to the action, while most of the fleet HQ was in Plymouth.
The most famous commander of the Western Approaches was Admiral Sir Max Horton, who took command in November 1942 and immediately instituted a series of tactical changes in the way the escort ships were to be used. Organizing them into "support groups" and "hunter-killer groups", they were to operate at longer distances from the convoys and prevent the deadly wolfpacks from ever forming. The technique was successful: with more forces becoming available, rapidly improving technology (particularly radar), and information being provided by Ultra, the battle was soon over with the Allies successful.
See also: GIUK gap