Naive Bayes guesses the answer using probability — it asks "how likely is this, given what I've already seen?"
Imagine it like this: If you see storm clouds, you think "rain is likely." If on top of that you feel the wind pick up, you think "rain is even more likely." Naive Bayes adds up clues like these to guess the most likely answer — it's called "naive" because it treats each clue as if it didn't affect the others, a simple but surprisingly useful shortcut.
Examples:
So? Naive Bayes is fast and simple, and it's especially good at sorting text — like telling spam apart from real messages.