It depends on the specifics of the external application, mainly: 3rd party or is it something you have control over?... what it's built with, what it's capabilities are, etc.
A 'kludgy' method would be to simply use the file system and have Java watch for files dropped in a specific location (taking care to handle locked files appropriately). A more sophisticated method would be to communicate via sockets, or writing to a database table within a local/internally hosted db such as hsqldb. Using in/out streams via java.lang.Process might also do the trick, depending on the 3rd party app of course.
But again all of this depends on the specifics of the application you're communicating with. Java's Process class isn't going to help if the 3rd party app is Excel (in which case you'd probably have to watch a save directory for xls files per the first method I mentioned).