An Attempt to Understand Boosting Algorithm(s)

Last tuesday, at the annual meeting of the French Economic Association, I was having lunch with Alfred, and while we were chatting about modeling issues (econometric models against machine learning prediction), he asked me what boosting was. Since I could not be very specific, we've been looking at wikipedia webpage. One should admit that it is not very informative. But at least, there is the idea that'weak learners' can be used to provide a good predictor. Now, to be honest, I guess I understand the concept. But I still can't reproduce what I got with standard'boosting' packages.