Message Persistence is a storage service that allows the storage and retrieval of messages published on PubNub, enabling real-time access to message history, with timestamps accurate to 10 nanoseconds, across multiple geographical data centers. Users can configure message retention for varying periods or indefinitely, and devices can access messages published while offline. The service allows for message deletion from history, but only for SDK clients initialized with a secret key. Users can enable Message Persistence through the Admin Portal by accessing the apps tab, selecting an application, navigating to the keysets page, and adjusting settings such as Retention, Delete-From-History, Delete Message Webhook, and presence event storage.