Sic
[sic] is often mostly pointing out that this is not an error in transcription, it is intentionally reproduced exactly.
It's mostly used around literal quotation, pointing that we left unusual/archaric/bad grammar/speclling but we're leaving it as-is.
It is sometimes also used for things that are suprising for other reasons - suggeciently weird reasoning, or things that seem to come out of nowhere.
It seems discouraged to use this for dialects and other less-usual-but-entirely-established use.
The square brackets you often seem to see this in seem to be a convention of editors to mark that they altered something inside the text (also e.g. used to make mild edits to make the grammar work in the context, insert [...] to note omission, etc.)
Some style guides also insist on italicising it.
sic itself just means 'thus' and is used in various phrases.
In this case it is a shorthand for sic erat scriptum (something like 'thus was it written'), but almost no one would know that.