While synchronism and synchronic are much older words, Synchronicity is a word from Carl Jung. My understanding is that during his mystic phase he used it to make sense of ideas like the astrologer's dictum 'As above, so below.'
It's a common experience in certain mental health conditions to see messages and portents in phenomena. It's reasonable to see this as an extension or extra emphasis on our pattern-seeking faculty, which we see in pareidolia, like seeing faces in clouds, and it has been suggested this s involved in religioys behaviours, eg Faces in the Clouds: A New Theory of Religion (PhilPapers journal article). Robert Sapolsky makes a great case in his lecture on Biological Underpinnings of Religiosity, that what we think of now as schizo-spectrum and obsessive-compulsive disorders are the extreme end of spectrum that has a functional role, allowing people's conscience or intuition to powerfully compel them to speak up or act, or to create rituals and shared experiences that help bind people together (see Durkheim's theory of religion).
The more challenging thing yo recognise, is that what we call causality is only our best guess at narrating events. See: Is the idea of a causal chain physical (or even scientific)? A great deal of what we call causality, is about creating tractable models, those just good enough to give useful predictions or inferences. We are very prone to mistake that, for a deep understanding of things. See Cartwight's book How The Laws of Physics Lie.
Many areas of human endeavor, like composing music, tap in to ways to organise experience which is not based on a physicalist-materialist analysis of the past to make predictions. I see synchronicity above all as the simple recognition that we don't have to approach our lives entirely as scientists, we can do so as painters, we can see our life as more like a piece of music, than an equation being solved.
We can point to this as a way out of Turing's Halting Problem: we are not forced to exhaust the iterations established when we were 'coded'; unlike a computer we can alter our own code on any whim, by an ordering principle acausal or not.
This, especially factoring self-reference to decide who to be, in light of outcomes that will create, can create the Tangled Hierarchies of Hofstadter's Strange Loops - what he sees as the defining quality of minds, to be able 'recode' on the fly. See: Why does Man ask Why questions?