Bayes' theorem relates two conditional probabilities: P(A | B) = P(B | A) x P(A) / P(B). It lets you update a probability in light of new information. In particular, it shows that a reliable test can produce many false positives when the condition being tested for is rare.
Example
A rare disease affecting 1% of people and a test that detects 99% of sick people with 5% false positives: a positive test gives about a 17% chance of being sick.