Advantages
It is easy and fast to predict the class of the test data set. It also performs well in multi-class prediction.
When assumption of independence holds, a Naive Bayes classifier performs better compare to other models like logistic regression and you need less training data.
It perform well in case of categorical input variables compared to numerical variable(s). For numerical variable, normal distribution is assumed (bell curve, which is a strong assumption).
Disadvantages
If categorical variable has a category (in test data set), which was not observed in training data set, then model will assign a 0 (zero) probability and will be unable to make a prediction. This is often known as Zero Frequency. To solve this, we can use the smoothing technique. One of the simplest smoothing techniques is called Laplace estimation.
On the other side naive Bayes is also known as a bad estimator, so the probability outputs are not to be taken too seriously.
Another limitation of Naive Bayes is the assumption of independent predictors. In real life, it is almost impossible that we get a set of predictors which are completely independent.