This surprisingly common conversation expression is used when the person you are talking about suddenly appears, as in the following dialog:
Two friends are talking at a café. Alan: I heard that Tony wasn’t very happy at work today. Bill: Yeah. I’m not sure why? (Tony comes into the café) Alan: Ah, speak of the Devil. Here’s Tony now. Let’s ask him.
This idiom is the shortened form of the old proverb, “Speak of the devil, and he will appear.” Direct translations, or sayings with very similar meanings, can be found in numerous languages around the world. In Japanese, people may say "うわさをすれば影” (uwasa o sureba kage), which translates to "Gossip (about someone) and (his) shadow (will appear).