This world is a simplistic testing environment largely inspired from the http://codingbat.com invented by Nick Parlente.
The typical exercises are very short ones, aiming at improving the tactical programming abilities of the students. That is to say that you will be presented a quite long list of very little exercises about rather simple things. The idea is to train you on these issues until they become automatic to you.
In contrary to the other worlds, the BatWorld does not provide any fancy abstraction nor visualization. You have to fill a function, which gets called for a bunch of parameter sets, and that's it.
For more information, you should refer to the CodingBat.com documentation, which contains for example a very useful documentation on boolean operators: http://codingbat.com/doc/ifboolean.html