The rule for updating what you believe when new evidence arrives. It says the strength of your new belief depends not just on how good the evidence is but on how likely the thing was to begin with. It is the reason a positive result on a test for a rare condition is often still probably wrong.
Technical view
The posterior is proportional to the likelihood times the prior. It underpins Bayesian inference, naive Bayes classification, and the framing of learning as updating beliefs over parameters given data. Practically its most valuable use is diagnostic reasoning about classifier outputs under class imbalance, where ignoring the base rate produces confidently wrong conclusions.
Related
Part of AI Terminology Index, section: Maths and Statistics.