How did implementing the Jewish badge help the Nazis?

Of course the obvious benefit of the badge to the Nazis was the visual labeling of the Jews. No longer would the rabble only be able to attack and persecute those Jews with stereotypical Jewish features or forms of dress, now all Jews and part Jews were open to the various Nazi actions.

The badge made a distinction. One day there were just people on the street, and the next day, there were Jews and non-Jews.

A common reaction was as Gertrud Scholtz-Klink's stated in her answer to the question, "What did you think when one day in 1941 you saw so many of your fellow Berliners appear with yellow stars on their coats?" Her answer, "I don't know how to say it. There were so many. I felt that my aesthetic sensibility was wounded."⁶ All of a sudden, stars were everywhere, just like Hitler had said they were.

What about the Jews? How did the badge affect them?

At first, many Jews felt humiliated at having to wear the badge. As in Warsaw:

For many weeks the Jewish intelligentsia retired to voluntary house arrest. Nobody dared to go out into the street with the stigma on his arm, and if compelled to do so, tried to sneak through without being noticed, in shame and in pain, with his eyes fixed to the ground.⁷

The badge was an obvious, visual, step back to the Middle Ages, a time before Emancipation.
But soon after its implementation, the badge represented more than humiliation and shame, it represented fear.

If a Jew forgot to wear their badge they could be fined or imprisoned, but often, it meant beatings or death. Jews came up with ways to remind themselves not to go out without their badge. Posters often could be found at the exit doors of apartments that warned Jews by stating: "Remember the Badge!" Have you already put on the Badge?" "The Badge!" "Attention, the Badge!" "Before leaving the building, put on the Badge!"⁸

But remembering to wear the badge was not their only fear. Wearing the badge meant that they were targets for attacks and that they could be grabbed for forced labor.

Many Jews attempted to hide the badge. When the badge was a white armband with a Star of David, men and women would wear white shirts or blouses. When the badge was yellow and worn on the chest, Jews would carry objects and hold them in such a way as to cover their badge. To make sure that Jews could be easily noticed, some local authorities added additional stars to be worn on the back and even on one knee.

But those weren't the only rules to live by. And, actually, what made the fear of the badge even greater were the other innumerable infractions for which Jews could be punished. Jews could be punished for wearing a creased of folded badge. They could be punished for wearing their badge a centimeter out of place. They could be punished for attaching the badge using a safety pin rather than sewing it onto their clothing.⁹

The use of safety pins was an effort to conserve badges and yet give themselves flexibility in outfits. Jews were required to wear a badge on their outer clothing - thus, at least on their dress or shirt and on their overcoat. But often, the material for badges or the badges themselves were scarce, so the number of dresses or shirts that one owned far exceeded the availability of badges. In order to wear more than one dress or shirt all the time, Jews would safety pin a badge onto their clothing for easy transfer of the badge to the next day's clothing. The Nazis did not like the practice of safety pinning for they believed it was so the Jews could easily take off their star if danger seemed near. And it very often was.