Compile means that you need the JAR for compiling and running the app. For a web application, as an example, the JAR will be placed in the WEB-INF/lib directory.
Provided means that you need the JAR for compiling, but at run time there is already a JAR provided by the environment so you don't need it packaged with your app. For a web app, this means that the JAR file will not be placed into the WEB-INF/lib directory.
For a web app, if the app server already provides the JAR (or its functionality), then use "provided" otherwise use "compile".