What is it?

Client:: The client part of a client-server architecture. Typically, a client is an application that runs on a personal computer or workstation and relies on a server to perform some operations. For example, an e-mail client is an application that enables you to send and receive e-mail. (source: www.webopedia.com).
MUD:: MUD stands for Multi-User Dungeon (or Dimension) and refers to a type of text-based online game in which multiple players can interact with each other through their characters in a shared environment.
MUD Client:: A MUD client is a specialized telnet program for use with mudding. Such a client is capable of all regular telnet activities, but adds additional features specifically designed to make mudding easier. These features typically include long scrollback, command line entry fields (allowing one to edit the command line before sending it), aliases, triggers, macros and configuration save files.
Telnet:: A terminal emulation program for TCP/IP networks such as the Internet. The Telnet program runs on your computer and connects your PC to a server on the network. You can then enter commands through the Telnet program and they will be executed as if you were entering them directly on the server console. This enables you to control the server and communicate with other servers on the network. To start a Telnet session, you must log in to a server by entering a valid username and password. Telnet is a common way to remotely control Web servers. (source: www.webopaedia.com).