The Bayesian filter breaks down each message into words or "tokens" and computes a spam score for each token. Some tokens appear frequently in spam messages, while other tokens appear more frequently in good messages. Because your email is different from anyone else's email, your good tokens will be unique to you and very difficult for a spammer to spoof. The score of each token in a message is combined to create an overall spam score for that message.
You can train the Bayesian filter by correcting the decisions it makes. If Spamfire thinks a message is spam, you can correct it and tell Spamfire that the message is good. When you do this, Spamfire adjusts the scores for all the tokens in that message. This will improve Spamfire's ability to recognize future email messages that share those tokens.
Best of all, Spamfire can automatically train the Bayesian filters with results from other filters, such as Remote Filters and Sender Filters. Auto-training means that Spamfire can become very accurate, very quickly with very little assistance from you.
You can view your Bayesian tokens and make some settings on the Bayesian Filter Preferences Window.