Is this word part of your active or passive vocabulary? Do you ever use it at all? If yes, could you please give me some real-world examples related to how one would use this word in conversational English? I assume this is not a very common word to use, but at the same time it's very difficult to make sense of the definition lists they've got in the dictionaries because all the definitions there seem to be slightly different from one another.
It is part of an educated (university-level) vocabulary, and can be used as a segue in a meeting, when the topic is going to change abruptly.
[Let's assume we've been talking about sales in the Euro Zone up to this point]
Apropos the Pacific Rim, we've appointed Cookie Monster head of emerging markets.
Apropos is not a very common word in English. But it's not rare either.
Short and sweet meaning of apropos is appropriate.
You can learn this by saying
"How apropos!" when you mean to say "How appropriate!" (when you agree with someone on something)
"apropos" is a foreign word; I believe the most common use of this word is to indicate that someone has said something that sort of comes out of nowhere---hence the common expression "apropos" of nothing"--meaning--even tho we had been talking about X, Stella opened her mouth to comment on Y.