Tiles are the square or rectangular objects on the start screen that represent applications. They can be a simple display of an image and/or text or an application can make them display information from the application (like the latest tweet or current
weather).
Charms are the icons that appear to allow an application to communicate (share) information with other apps. If you are on a non-touch device, Windows_Key + C will bring up these icons in an app that supports such functionality.
There are some great videos here with more information:
http://channel9.msdn.com/Events/Build/Build2011