A MicroStation InitApp is a non-interactive app that is started using the Windows command-line -waAppName switch, or is listed in the MS_INITAPPS configuration variable.
The V8 SDK provides an InitApp example, but it didn't make it as far as CONNECT. I've written InitApp CONNECT Edition for anyone interested. It's a C++ app.
The code is almost entirely new, making use of MicroStationAPI classes and other functionality that didn't exist in the V8 era.