The Luftwaffe was the aerial warfare branch of the German Wehrmacht during World War II. After the German Empire's World War I-era army air force, the Luftstreitkräfte, and naval air units had been disbanded under the terms of the Treaty of Versailles the Luftwaffe was reformed in 1935 and grew to become one of the strongest, most doctrinally advanced, and most battle-experienced air forces in the world when World War II started in Europe in September 1939. After the defeat of the Third Reich the Luftwaffe was disbanded in 1946.
Luftwaffe is also the generic term in German speaking countries for any national military aviation service, and the names of air forces in other countries are usually translated into German as "Luftwaffe" (e.g. Royal Air Force is often translated as britische Luftwaffe). However, Luftstreitkräfte, or "air armed force", is also sometimes used as a translation of "air force". And because Luft means "air" and Waffe may be translated into English as either "weapon" or "arm", "Air Arm" may be considered the most literal English translation of Luftwaffe (cf. Fleet Air Arm).
Read more about Luftwaffe: Spanish Civil War, Second World War, Luftwaffe Ground Forces, War Crimes