The name Jabber is actually the original name for the IETF XMPP protocols (RFC 3920-3923). Since Jabber is by far a better name than XMPP, the original name has stuck. This protocol was originally designed to be a decentralized, nonproprietary, open-standards messaging and presence framework. It supports offline message delivery and encryption, and has grown to include voice messaging, which Asterisk supports.
It is interesting to note that in the beginning, Jabber was seen as a competitor to the SIMPLE protocol, which is SIP-based. XMPP is designed as a more general protocol, and is of course XML-based.
Asterisk can be configured to utilize XMPP in several capacities. It may utilize XMPP as a presence framework (e.g., Extension 205 is away or on the phone), or, through the voice messaging framework JINGLE, support full voice communications with other services such as Google Talk.
Unlike other messaging networks such as MSN and Yahoo!, XMPP is decentralized. Anyone may have his own Jabber server and run any number of services on his server. You send messages in much the same way that you send email: the Jabber server you use contacts the Jabber server of the other person, and a direct connection is established. If the other person is not online, the message is stored, and when she log in to her Jabber server, any stored messages are delivered. With encryption (the XMPP protocol supports TLS), it is no wonder why many businesses are starting to implement their internal messaging networks using this amazing protocol, and Asterisk is able to seamlessly integrate into this communications network.