The MSTR Web that everyone uses to access any application (developed in MSTR) has been developed using Web API.
Web API allows an interface with the Intelligence Server. The API consists of numerous functions and calls written in Java which the Intelligence Server can understand. These calls include "Login to Project", "Execute Report", etc etc etc.
Externally this API exposes simple functions that can be invoked using VB Dlls and/or directly from ASP. You do not have to worry about any of the Java API calls.
Hope this helps.
You can get a reference to this if you have installed MicroStrategy on your desktop.
Follow the clicks
Start->Programs->MicroStrategy7->SDK->Documentation->Java Web API Reference