What are the extra capabilities Python gives when used with Java?
In general, there are no (overall) benefits for doing this. You're simply adding in another language with its own set of runtime features, that, for the most part does the same things that you can do in Java. Unless you have specific reason to add Python integration into your Java application, it would be a very poor idea to do so.
However, in some cases there are reasons why you might want to do this:
To add scripting capabilities to your application.
If you want the end users of your application (or perhaps authors of add-ons, or system administrators) to be able to script parts of your application, then Python is a reasonable choice to offer them. There are other good choices too, but Python is fairly well known, quite mature, has decent Java integration and a good set of features, so it's not a bad choice.
To accommodate Python developers in your team
If your team has Python developers who (for whatever reason) aren't willing/able to write in Java, then you can provide facilities to support including their code in your Java application.
If you believe that writing in Python is more productive
If you/your team believe that writing Python code is sufficiently more productive than writing Java code to justify the cost of integrating the Jython runtime into your Java application, then you might take that path. Personally, I'd question that decision in all by the most niche of use cases, but that's up to each team to decide.
To integrate with existing Python code
There may be libraries or tools that are written in Python that you want to integrate with in your application. Rather than re-writing them in Java, or trying to run them via the command-line, it might be a good idea to run them in the Jython environment in the JVM.
Unless you have a specific reason like one of those listed above, then simply integrating Jython into your application isn't going to give you any benefits, it will simply be extra effort to write and support. If you have one of those reasons, then it might make sense, it will depend on your circumstances.
I am a Java developer. I would like to know what capabilities and/or positives I can add to a Java application, by including Python as a development language.
I am posting this here as I am not getting a good answer from google. I would request that you don't vote down, marking it to be a descriptive question, so that a future Java developer can understand how he can make an application better with Python.