"Explicit knowledge" is knowledge that's easy to convey to other people; it's portable and shareable.
Knowing that yeast is what usually causes bread to rise is explicit knowledge, as is knowing that 2 + 2 equals 4 (as is understanding how math works more holistically).
Tacit knowledge is a more ingrained, less-shareable type of understanding.
If you drive an old but familiar car every day, there's a good chance you have a lot of tacit knowledge about how that car functions in various circumstances that you wouldn't necessarily be able to put into words, but you know these things reflexively and intuitively, nonetheless.
The same is true of cultural norms within cliques and organizations, how to create a specific vibe in a new work using a familiar art medium, and what it is about the initial fraction of a second of a familiar song that tells you what you’re about to hear.
Tacit knowledge is often invisible to us unless it's pointed out by someone else, or unless we're attempting to convey that knowledge (often unsuccessfully) to another person.
Instead of direct transmission, this knowledge tends to be communicated via things like subtle social cues, repetitive physical practice of a skill or trade, or repetitive interactions with a person, activity, or field of knowledge.
This organizational concept was originally posited back in the mid-20th century by a British polymath named Michael Polanyi, but it was later expounded-upon in a 2010 book called Tacit and Explicit Knowledge, in which the author, a British sociologist named Harry Collins, suggested that there are three primary categories of tacit knowledge: relational, somatic, and collective.
Relational tacit knowledge, according to his definition, is buried in our interactions with other human beings.
So when we understand that we should adjust our tone around certain authority figures, or that some people prefer to text rather than talking on the phone (without really realizing these are data point we've accumulated), that's relational tacit knowledge.
Somatic tacit knowledge is related to our understanding of our own bodies.
When we play an instrument, engage in a sport, balance ourselves on rocky terrain—our casual performance of these complex tasks are examples of somatic tacit knowledge; it's unlikely we'd be able to easily communicate how and why we decided to balance ourselves in precisely the way we did when walking over a jagged piece of sidewalk, and yet our bodies and brains know exactly how to do so, when warranted.
And collective tacit knowledge is the jumble of understandings injected into our social spaces, both in the norms to which we adhere and the physical spaces we occupy.
So the understanding that folks tend to aggregate and be open to a few minutes of conversation at the office water cooler, and the understanding that a chapel will tend to be a place for quiet, not for playing loud music (and the visual cues we look for to understand we’ve walked into a chapel), are examples of collective tacit knowledge.
Importantly, these flavors of tacit knowledge, and the concept of tacit and explicit knowledge, more holistically, are debatable and prone to bleeding into adjacent categories, and by their very nature are mostly an exercise in indexing and labeling—they’re not hard-set psychological or cultural rules, and they aren’t the type of science we can test or prove.
That said, having organizational systems like this one available can help us notice some of the assumptions and reflexes that guide our behaviors, and can sometimes help us recognize and manage our knowledge and how we communicate that knowledge to others.