What does it mean?
It means you belong to certain communities. Usually.
What goes along with wearing one?
Not necessarily anything. You should get to know the person if you want to find out.
What do you answer to people in shudduchim who say that they don’t want to be judged by what they wear.
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I just really want to know halachos behind it. minhagim behind it. etc.
I would think it is a minhag at this point. But I’ll let the other posters tell you about that.