"Boolean" in general just refers to a variable that has two values, conventionally labeled true and false. Rule Machine has a "private Boolean" built in to each rule. Here "private" means that the variable belongs only to that rule (often "private" means that it can't be accessed from elsewhere, but that's not quite true: other rules can modify the PB of another rule).
How you use it is up to you. The effect would be little different from if you just created your own variable (and you can indeed create local variables, including a Boolean, within a rule, or a global Boolean variable accessible from all rules). There are a few examples in the docs (which I recommend reading), one of which is to track whether your actions have already run and then not do them again until you "reset" the variable. You can use it to track anything you want as long as two possible values are sufficient.
Also, a small history lesson: in old versions of RM, PB did something on its own: your rule just wouldn't run if it was false. In modern RM, you must do something with it--e.g., check its value with an IF in your actions--to create whatever effect you want. So, be careful if you find any pre-Rule-4.0 examples. 
