Synchronicity is a term that people are either gung-ho about, or vehemently reject. I suppose I should mention a third group that has no clue what the word means, so let’s start with them.
Synchronicity is a term credited to Carl Jung, and it defines a simultaneous occurrence of events that are highly significant, yet have no obvious or likely connection. “Meaningful coincidence” is a simpler way to describe it.
Pretty much everyone has a good story about a bizarre coincidence. The difference between what gets labelled a synchronicity versus a coincidence is the meaning attached to the event. For the die hard skeptic, no matter how impossibly unlikely their tale of coincidence is, they will never connect anything more to it than random chance. At the opposite end of the spectrum, the overzealous New Ager sees absolutely every mundane occurrence as reason to declare synchronous incredulity to anyone who’ll listen.