The purpose of the Web API is to provide you with the possibility to program any logic that is not available within OVSD. You program this logic using Java.
The API itself simply allows you to search, read and write to any field in any object, as well as to create and delete relations amongst objects. The API provides a very large number of classes, corresponding to all these fields, as well as a few basic methods per class, as mentioned above.
Basically, you can run your Java on the client or on a server, allowing you to read from and update your data. You use the relevant actions of the UI and DB rules to do this.
In addition to being able to code in Java, you need to know how to set up the server (be it Tomcat, or some other java server, such as WebLogic); and you need to know how to recompile the API, in case you create new custom fields.
Since you create java programs, you can do virtually anything you like at the system, I/O or logic level.
The answer to your last question is "sort of". Remember that you must call the interface from a rule, so it does not entirely replace rules.
Finally, remember that OVSD is a lame-duck product. Everything that you invest in building Java functionality using the Web API will be lost when you migrate to ver. 7 (or to some other product). Make sure your functions are extremely well documented, because you are going to have to create the functionality again in a new environment.