It's a internal CICS mirror program in each CICS-product and handels inbound function shipping.
A function shipping request takes the form of a normal EXEC CICS command. If either of the following conditions applies, the application-owning system recognizes that function shipping is required and ships the request to the remote resource-owning system.
It's invoked by CICS-File-Control and LUTYPE6.1-Architected-Processes.
DFHMIRS -> Mirror program
An architected process is an IBM defined method of allowing dissimilar products to exchange intercommunication requests in a way that is understood by both products.
Architected processes are:
CICS file control model
System message model
Synclevel 1 mirror
APPC sync level-1 mirror
The architected processes implemented by CICS are:
System message model for handling messages containing various types of information that needs to be passed between systems (typically, DFS messages from IMS)
Scheduler model for handling scheduling requests
Queue model for handling queuing requests (in CICS terms, temporary-storage or transient-data requests)
DL/I model for handling DL/I requests
LU services model for handling requests between APPC service managers.
For more information read the Systemmanual please.