In traditional interviews, you are asked what your strengths and weaknesses are, what skills you bring to the table, etc. In a behavioral interview, the interviewer wants you to tell her HOW you've demonstrated those capabilities in your career. An interviewer wants to see how you actually handled a specific situation in the past rather than have you tell him how you would handle it in the future. He might ask you to describe a situation in which you felt you were wrongly criticized and how you handled it or how you remedied a near-miss on a deadline.
Here's a site that explains how interviewers use behavioral interviews to evaluate candidates and how best to answer the questions they put forth.
Another site offers an exhaustive (and I do mean exhaustive) list of behavioral interview questions that a hiring manager might ask. Going over them is a good way to prepare for an interview (or send your brain into meltdown, whichever comes first). The questions are divided into skill areas, and run the gamut from your your personal adaptability, to your time management style, to how you handle stress. Check it out here.