Bayesian probability
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You can find a mostly ELI5 explanation in the opening paragraph of the wiki article here: https://en.wikipedia.org/wiki/Bayesian_probability?wprov=sfla1
“Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification of a personal belief.”
Basically, the reason people use the term Bayesian is because schoolbooks teach probability as stuff associated random events, or multiple experiments. That’s a simple explanation, but results in a bunch of contradictions or confusing questions. Instead it’s more robust to think of probability as a quantification of one’s state of (usually incomplete) knowledge.
To take an example which I found helpful: let’s say I have a coin, which I guarantee to you, is perfectly biased (i.e. it will always land on the same side when flipped). However I don’t tell you if it’s biased to land on heads, or on tails (i know it, but i don’t tell you). Now what’s the probability it will show heads when flipped?
If you think about it, it’s still 0.5.
The coin throw, or the coin itself isn’t random. What’s incomplete is your information about the coin.
The term Bayesian comes from the mathematician Bayes, who is also responsible for Baye’s theorem. Bayes theorem is a very important theorem in probability, and life in general, given the increasing use of questionable statistics to promote misinformation in modern media.
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