The SMSC (Short Message Service Centre) is the carrier system that stores and forwards SMS, retrying delivery until the handset is reachable or the validity period ends.
Every mobile operator runs an SMSC. When a message arrives for one of its subscribers, the SMSC tries to deliver it; if the phone is off or out of coverage, it stores the message and retries on a schedule until the validity period expires. It is also the system that generates the delivery receipt when the handset acknowledges.
Gateways talk to SMSCs, directly or through aggregators, over protocols such as SMPP. The store-and-forward behaviour explains why a message to a switched-off phone can arrive hours later, and why "sent" is not the same as "delivered".
At SMSMeteor: the default validity is 48 hours; a message not delivered by then is marked expired, and the report says so.