Insignia show that you belong to a group, or an office, or that you have certain responsibilities.
They might be a sign of belief:
illustration by René L'Hôpitalor function:
This Red Cross nurse was called Iola.
They show what you stand for. They make clear why you are in a place. They indicate that you are acting on behalf of a group, and not individually.
A man with a gun who's wearing clothes with insignia on them is probably a soldier (or perhaps, though very rarely in England, a policeman).
A man with a gun who is not wearing insignia...
...I'm afraid I don't know how you can tell what he is.
How could anyone?
Spot the frippet: insignia. This word comes from Latin, from insignis, which means distinguished by a mark, or prominent. The Latin signum means mark.