Perhaps I am not an expert in this interface,from my experience and basic understanding of S6a interface I have replied.
Prior to answer your question we need to know the historical background of MME Evolution.
As we know in 2G/3G network the SGSN used to does the same work what MME does in LTE.
But in LTE network SGSN splits into two parts one to control Data Session (MME) and other to control User Packets(S-GW).
In order to allow a GPRS flow the MME needs to have few information, such as :-
1. Keeps track of UE that is registered to the network.
2.Acts as GateKeeper,Handling user Request for network access,setting up and tear down data sessions.
3.Handles the authentication of users on the network as well as authorization.
1.MME keep updating the UE location with the HSS by providing the Identity details(the MME-Identity is received within the Origin-Host AVP).
2. IMSI detail is mandatory in order to check the registered SIM card details.
3. Terminal Information (IMEI)
4. Visited PLMN Id
If all the above parameters are fine then HSS would reply with Subscription Data
All the above parameters are necessary to keep track of UE and UE Subscrption ,so that HSS needs to be aware of.