The change log for Apache POI is available online. To see the changes between 3.8 and 3.9, look between here and here
Unless otherwise detailed in the release notes included in the download, you should be fine to just drop the new jars in, in place of the old ones. Make sure you really remove the old ones though! You get all sorts of odd things going wrong if you have both old and new POI jars on your classpath