Usually Ue triggers service request message towards MME as a counter action of paging message. When MME receives "Downlink data Notify" message from SGW. MME sends "Downlink Data Notify Ack" to SGW. As part of this procedure, MME initiates Paging message for that UE. Once UE receives paging message, based on the type of paging message, UE sends either Service request message or Extended service request message. Here type of paging message means either paging has been received from CS domain or PS domain.
Whereas, MME can initiates service request itself due to HSS intervention like UE-subscription deleted etc.
Suppose HSS has asked to MME to initiated detach for a UE, which is in Idle mode. In that case, this procedure is known as "Network triggered service request".