Multi-User Chat (MUC) is an XMPP protocol extension for multi-user text chat, whereby multiple XMPP users can exchange messages in the context of a room or channel, similar to IRC. In addition to standard chatroom features such as room topics and invitations, the protocol defines a strong room control model, including the ability to kick and ban users, to name room moderators and administrators, to require membership or passwords in order to join the room.
Similar to, but less widely used than IRC, Multi-User Chat (MUC) is an XMPP protocol defined by XEP-0045:
This specification defines an XMPP protocol extension for multi-user text chat, whereby multiple XMPP users can exchange messages in the context of a room or channel, similar to Internet Relay Chat (IRC). In addition to standard chatroom features such as room topics and invitations, the protocol defines a strong room control model, including the ability to kick and ban users, to name room moderators and administrators, to require membership or passwords in order to join the room, etc.
A common, open-source implementation of XMPP is the Smack API. For Android, there is also the aSmack API, but this is being merged into Smack to unite the forked APIs.
Usage examples of a MUC can be found here.