A function performs a specific task. The task can be as simple as capitalizing the first letter of every word in a line of text or as complex as creating an array.
There are three types of functions: system functions, which are built into Authorware; scripting functions, which you create in Authorware; and custom functions, which include scripting Xtra extensions, U32s, and DLLs. Macromedia supplies a small set of custom functions with Authorware; many more are available from other developers.
The only real difference between system and custom functions is where they come from. They all have the same purpose: to increase the flexibility of Authorware and to extend the range of things you can accomplish.