I spend a great deal of time on this blog talking about the origins of garments, and what they might symbolize to the character- but the truth is, many characters will not be consciously aware why they are wearing these things, no matter how much of a costuming nerd the player might be.
Unless, of course, your character is a member of a priesthood.
Religion, nearly by definition, involves the use of symbols. Who can use these symbols, and when, may be fast and loose or highly formalized; it depends, to some degree, on how formal the religion itself is.
For example, a priest of the Orthodox church has no fewer than thirteen components to their official robes, each with a specific origin and purpose. (To see them in action, click here.) Being aware of these symbols is a part of the role of the clergy; they could not teach the laypeople their importance if they did not know them themselves. If your character is a member of a religious order, it is highly likely that some or all of their garb will have specific religious meanings that the character should know. Whether they do, of course, is variable; there can be delinquent friars in any universe.
Note: When you’re buying garb for a religious costume, you might want to do some research before purchasing actual religious materials. There are some pretty (if quite expensive) things available online, but they may not be meant for secular use. I generally hold the rule that I don’t mind if I offend, but I do not want to hurt; if you are of a similar mind, then take the time to consult with an authority from the religion you’re appropriating to get a sense of what their opinion would be on their garb being re-purposed as your larping gear.
Image credit: By Laurits Tuxen (1853-1927) [Public domain], via Wikimedia Commons.
PS Orthodox Church garb featured by a special request from Fair Escape!