When an instance arrives to a Message Wait event it waits there until the specified event occurs. If the Message Wait event is connected to the process flow by a due transition, the instance leaves the Message Wait activity when the due transition expires.
When the Message Wait event receives a notification from another process or application the Process Execution Engine performs the Argument mapping and then moves the instance to the next activity in the process flow.
If the Message Wait has the property Allow Interruptions enabled, the Message Wait is not part of the process flow. The Engine is constantly monitoring for an event to occur. When this event occurs the Engine pulls out from the process flow the instances that match the criteria specified in the notification. Then the instances flow through the Message Wait flow and once they get to the last activity they are sent back to the main process flow.