It's an abbreviation for "for your information," and while abbreviations can be capitalized, it's generally considered more casual and less formal to use them in lowercase.
Here's a breakdown:
* Formal: For your information.
* Informal: FYI
The best approach is to consider the context and tone of your communication. In formal writing, you might opt for the full phrase "for your information." In informal settings, lowercase "fyi" is perfectly acceptable.