Hi Sanat,
the AppointmentReplicationInitiatedByExternalIn is an inbound service. This means that this webservice should be called by an external system, maybe to create an appointment as a copy an existing appointment on an external system.
If you want to call an external webservice (on PI for example) you need to integrate an external webservice in your solution, and then in the event-beforesave of the standard bo, you call this interface and you pass all the needed values to the external system.
In the official developers guide you can find all the related informations.