Naive Bayes classifiers makes the naive assumption that the features are independent. They make use of Bayes theorem.
Naive Bayes classifiers make use of Bayes theorem:
$$\overbrace{P(c | X)}^{\text{A posteriori}} = \frac{\overbrace{P(X | c)}^{\text{Likelihood}} \cdot \overbrace{P(c)}^{\text{A priori} } }{\underbrace{P(X)}_{\text{evidence}}}$$