This application is an environment tool of Java language. Detaily, this application execute your own java application through `Dalvik machine` which is a runtime for Android Application. Basically, every android applications are written in java language. So if your own `jar` file which is an executable form of java program is converted to the format of `Dalvik machine`, then theoretically the program should be executed well (although there may be platform-dependent libraries in the program).
`Java Manager` consists of compiling `.java` file to `.class` one, executing `.class` or `.jar` file and even decompiling the `.class` file.
As mentioned above, this application is based on `Dalvik machine` which is a default runtime environment of android system. So precisely `root` permission is not required. You can use this application without any `root` permission.