What is Wordpress-MU and how is it different from the Wordpress that people are more familiar with?
When people say "Wordpress" in general, they are talking about the single-user install version of Wordpress blogger software that you can download from Wordpress.org and install on your webhost. This install is designed to run a single blog.
People who do not want to purchase own webhosting nor perform their own installation of wordpress, can create a blog and start blogging in minutes at Wordpress.com -- notice this is at dot com whereas the Wordpress open-source software download is at dot org.
Wordpress.com is created by Automattic.com and it is runs on Wordpress-MU software that enables the creation of multiple blogs with one install of the software. So for example, a single Wordpress-MU install can run a blog at multiple sub-domains such as http://jack.example.com and another blog at http://jill.example.com and any number (limited to diskspace and bandwidth of your host).
Whereas in the single-user version, if you had two blogs, you would install two instances of Wordpress and the two blogs are run separately.
The Wordpress-MU software is based on the Wordpress software, but it is not identical. It is a fork of the Wordpress line and has changes in the database tables. Wordpress-MU is closed for user-contributions; Wordpress is not. The "MU" in "Wordpress-MU" stands for "multiple-users" and you can pronounce it as separate-letters as in "Wordpress M U". But if you go to Wordpress-MU site, you see that they use the Greek symbol letter Mu -- so you can also pronounce it "mew".
The various blogs run by Wordpress-MU can be run on sub-domains of a single domain name. There is a Wordpress MU plugin called Wordpress MU Domain Mapping that can allow Wordpress MU users (the bloggers on your Wordpress MU) to have their own domain name. This implementation may require the configure of a unique IP.
Some plugins that work for single-user Wordpress may not work for Wordpress MU -- especially plugins that alter or create tables because Wordpress MU runs off of one database. See Wordpress MU plugin compatibility.
Some themes that work for single-user Wordpress may not work for Wordpress MU -- especially when widgets are involvedref. Although users of Wordpress MU can select pre-defined themes, they can not edit their own theme. Since each theme is shared by all users using that theme, a theme change affects all users.
Wordpress MU is designed for running blog-farms like Wordpress.com where you have hundreds of separate blogs with different admins running each of them. If you are a single person with a couple of blogs, you would use the Single-User version of Wordpress and install two of them.
Even if you are running several blogs, you may be better off installing and using several versions of the the single-user version of Wordpress. This is because Wordpress-MU adds complexity and requires expertise with the single-user Wordpress before trying to learn Wordpress-MU. The install of Wordpress MU is not a simple install as in case for the single-user Wordpress. And Wordpress MU can not be installed with Fantastico. Subdomain blogs may require wildcard DNS. Some webhosts does not allow Wordpress MU to be run on "shared servers". You may be required to be on a "private server".
So if you are just starting out with Wordpress, start with single-user Wordpress (not with Wordpress MU).
Dreamhost Wiki provides some good points about installation of Wordpress-MU as well as questions to ask before deciding upon Wordpress-MU. One of the questions is "Are you creating more than five blogs with different admins? If not, you are probably better off with the single-user version of Wordpress.
References
Wordpress MU FAQs
Wordpress MU Codex
Wordpress MU documentation
