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http://www.amazon.com/Python-Standard-Library-Example-Developers/dp/0321767349

Basically the standard library in any language is a bunch of APIs that allow you to do stuff that you would have had to figure out how to code yourself. It's why things like github are so popular because you can go look at how someone else coded something and try to improve upon their API and sometimes these open source APIs turn out better than what is built into a language's standard library.

You said they know how to email, teach them about the email libs and show them how to build a program that will email something for them.

They are essentially identical.

function functName(...)

is referred to as a function statement whereas

var varName = function(...)

is called a function literal. You can also name the function in a function literal:

var varName = function functName(...) // useful for recursive functions.

Function literals are used (for example) when passing a function to another function.

Functions are covered in length in Chapter 8 of this book; my recommended resource for anyone serious about learning JavaScript.