The Nazi Salute, or Sieg Hail Salute, was used as a greeting in Nazi Germany, it was introduced by the Nazi's to Germany during the 1930's and its purpose was meant to show obedience and loyalty to the Nazi party's leader: Adolf Hitler.

The salute was mandatory for all civilians, however was moreover optional for military personnel for those who preferred the the traditional military salute, at least until the assassination attempt against Hitler in 1944.

Hitler himself utilized the salute in two ways: for civilians/crowds/troop reviews, he performed the regular Nazi Salute that you would see in many photographs with a straight arm, especially this one: https://foreignpolicy.com/2015/10/22/a-lesson-for-netanyahu-from-a-real-holocaust-historian/

The second way Hitler utilized the Nazi salute was for individuals, or one-on-one interactions. Let's say Heinrich Himmler and Hitler were in the same room, before engaging in conversation, Himmler would render the standard straight-arm Nazi Salute, and Hitler, acknowledging this, would render a bent-arm Nazi Salute, which looks like the image you provided.

Hitler was not the only official within Nazi Germany to be authorized a bent-arm Nazi Salute, it was allowed and even expected for high government/party officials to do so and Wehrmacht high command.

To put into perspective, think of it in a way as a standard military's way of saluting. An enlisted individual will salute the officer first, in response an officer will render a salute. In this case, we have a citizen/soldier saluting a high official and reaffirming their allegiance to Hitler, the response would be that high official returning the same salute, except with a bent arm.

EDIT: I will make note of this as I should have explained this a little further: the Nazi's did NOT invent the Nazi Salute; while yes obviously they did the name, the origins of this salute go back to Ancient Rome, to the Medieval Ages, and even to American school classrooms with the Bellamy salute to the American flag before the Nazi's even came to power.

EDIT 2: Added "to Germany" in first paragraph.