Just as resumes and cover letters have evolved, thank-you letters can help you stand out among other candidates when competing for a job. This is especially true if the future potential employer is on the fence about whether or not you will be a good fit for that organization.
The thank-you letter allows you another opportunity to further sell yourself and overcome any objections that they might have. In addition to highlighting what you took away from the interview and reiterating that you would be an excellent fit, you can also key in on problems that you may be able to solve based on your new insider knowledge. Take a look at this detailed thank-you letter and the example here. (Please excuse the direction as it is intended to be a teaching tool for practitioners towards their clients.)