Ben Cherry, web developer at Twitter, takes us step by step through the Module Pattern. He introduces the standard features of Anonymous Closures and avoiding global scope, and covers advanced concepts such as augmentation, cloning, inheritance, private state and sub-modules.
A simplified explanation of closures by Morris Johns: A closure is the local variables for a function - kept alive after the function has returned.
A stackoverflow community article explaining closures in plain simple English does a great job. Succinctly: a closure is created when inner function that gets returned. The inner function can still see the variables and methods defined in the outer function.
Tim describes another two different approaches to using the Module Pattern (a way of creating Singletons). The first example takes advantage of the natural indentation to clearly see which methods are private and which are public. The second is a curried function, a function that returns another function.
Christian Heilmann offers another incremental improvement to the Module Pattern, and calls it the Revealing Module Pattern. This defines an anonymous object that contains a list of methods and properties that are publicly available. Christian notes that this method also allows you to set up a public property that's privately generated by a method. Christian's improvement makes it quickly clear which properties and methods are public.
Douglas Crockford discusses how to create private members and methods, and using privileged methods to bridge the gap between public and private. It also contains the simplest and most understandable definition of closures I've ever seen.