Basically, the module cannot be instantiated. When a class includes a module, a proxy superclass is generated that provides access to all the module methods as well as the class methods.
A module can be included by multiple classes. Modules cannot be inherited, but this "mixin" model provides a useful type of "multiple inheritrance". OO purists will disagree with that statement, but don't let purity get in the way of getting the job done.
(This answer originally linked to http://www.rubycentral.com/pickaxe/classes.html
, but that link and its domain are no longer active.)