XMPP, often referred to as jabber, is a protocol for sending instant messages to other people and having group chats.
Unlike many chat protocols, xmpp is federated. That means there is no central server or organizations that controls it. It's more like email - anyone can setup an XMPP server and their users can communicate with any other server running software that speaks XMPP.
The easiest way to get started is to create a user account for each person in your group with chat enabled.
Then, instruct everyone to use our web client to login.
Any member of your group can create a group and invite the other users to the group.
Yes - if you don't want to chat via a web application, you can install another program, such as gajim or use conversations on your Android phone.