You can find multiple answers to that question, and I will try to distinguish them. At the very least, it is a movement of wearing a safety pin to show your support of minorities and your rejection of intimidation.
In summary, there seem to be 2 main reasons people decided to wear safety pins:
In both cases, you had a vote by the population which apparently at least seemed to support discrimination ideas.
In both the USA and Great Britain, some of the intolerance was against the Muslim population, but in the USA, you can add the Spanish speaking residents, the LGBT community and the African-American population.
For some, the Safety Pin protest is slacktivism: an empty gesture made by someone not affected by the issue in order to wash themselves of guilt.
For others, it is a promise to help any person victim of intimidation.
Some African-Americans have decried the protest as simply white people not understanding the issues.
The way I see it and the reason I wear a safety pin now, is that I want to show that I am a safe person who not only reject discrimination of all sorts and any forms of intimidation, but also, that I act when I see these injustices occurring.