This is an old revision of the document!
First thing to mention is that Jabber is now officially called 'XMPP'. I prefer to continue calling it Jabber as the name is much friendly than XMPP.
Jabber is a decentralized instant messaging (IM) service, meaning that there is no central server regulating it's use.
This differs from popular proprietary IM protocols such as AIM, ICQ, MSN Messenger, and Yahoo Messenger, which all must communicate, or at least establish a connection, via a central server. A Jabber user who wants to send a message to another user contacts his own XMPP server, which relays the message to the recipient's server. Only then is the message pushed to the recipient's client.
For this reason, Jabber addresses mimic email addresses, with each part of the address serving the same purpose as it's counterpart in an email address. Also for this reason, Jabber IM accounts can “look” different - there is no “@jabber.” syntax. This can lead to some confusion as to what is a Jabber account.
There are many Jabber servers available which provide free access to people who want to create a Jabber account.
Extensible Messaging and Presence Protocol (XMPP) is a communications protocol for message-oriented middleware based on XML (Extensible Markup Language). The protocol was originally named Jabber, and was developed by the Jabber open-source community in 1999 for near real-time, instant messaging (IM), presence information, and contact list maintenance.
Designed to be extensible, the protocol has also been used for publish-subscribe systems, signalling for VoIP, video, file transfer, gaming, Internet of Things applications such as the smart grid, and social networking services.
(This is an extract from the Wikipedia article on XMPP.)
Good question! Here is a list of software applications that support Jabber accounts.