MU* refers to things like the earliest multiplayer games, "Multi-User Dungeons." The original MUDs were often based on Rogue, which is the origin of the term and genre, Roguelike. Over time, they evolved to include many more features and people came up with versions that centered around roleplay, sometimes called MUSH (multi-user shared hallucination), MUX, MOO, etc. The easiest way to refer to them became MU*. (The star symbol was used as a wildcard character, to indicate you didn't want an exact search on early computers.)
MU* usually relies on the same kind of telenet clients that power IRC, but usually have additional feature to support things like dicerolls and a room. PennMUSH, DikuMUD and Evennia are examples of clients for creating MU* servers. Evennia is the most recent one, powered by Python so you can actually understand its code if you are using GDScript!
Graphical MUDs were the precursor to MMOs and a few are even still in operation decades later!
In fact, Everquest, the first game to be called an MMO used DikuMUD under the hood and actually got sued by the college that maintained it for not giving proper credit and therefore breaking terms of service!