The loanword apropos comes from the French phrase à propos de, meaning with respect to. In English, apropos is conventionally used as a preposition meaning with regard to, and it’s also an adjective for pertinent or to the point.
Apropos is often misused in place of appropriate. This sense of apropos has nothing to do with the original French phrase or the word’s conventional meaning. In such cases, appropriate is a perfectly good replacement. Still, this use of apropos is common that we might simply have to accept that the word has changed.
Apropos may be used alone or followed by of or to—for example:
So Veronique de Rugy has responded to Nate Silver apropos the matter I discussed yesterday. [Guardian]
Apropos of nothing, we would like to take a moment to remind all period action films that horses do not explode like that. [Geek-o-System]
Apropos is sometimes questionably used as a synonym for appropriate—for example:
Bedford-Stuy Projects Probably Not Most Apropos Place for Prison-Themed Playground [Village Voice]
With April being Earth Month, it is apropos to take a look at what the transportation world holds beyond the current range of hybrids. [Calgary Herald]