They were originally just called the P.08, but they are known as Lugers after their inventer's name.
The model we know today most popularly, is the Model P.08 Luger, introduced in 1908 as the standard sidearm of the German military. It deviated from previous lugers by eliminating the grip safety and being chambered in 9mm Parabellum, which is the 7.65 Luger casing redesigned to fit a 9mm projectile as requested by the Wehrmacht(German Army.)
The 9mm cartridge is used by the U.S. Military currently in the M9, and is the NATO standard pistol cartridge.
There were many manufacturers of Lugers, some of the most popular being Mauser, DWM, Kreighoff, and others. The German Army used a 4" Barrel version, which is most popular, while the Navy's version had a 6" barrel. Artillery crews had 10" barrels. Lugers have an 8 round capacity, however drum magazines made for the Artillery Lugers hold many more rounds.
Lugers were known to be extremely accurate, even by todays standards, due to the fixed barrel design. They operate off of the Maxim toggle action that the first machineguns used. Lugers were made to extremely high tolerances, and fit together with immense precision. Lugers with all matching parts and in good condition with original finish can be worth a lot of money today. In 1938, the German military was mainly producing the Walther P38 because it was a far cheaper design due to the lack of required hand fitting. Lugers were produced until the end of World War II however. Lugers are the first practical semi-auto pistols to be made, and were extremely influential in the world of handguns. They are also fabulously beautiful pistols and pieces of history and art, well sought after by collectors.