What's it all about, anyway?
ARexx might not be the world's best scripting language. In fact, it's quite dated by today's standards, even compared to Microsoft's VBScript. It's based on IBM's REXX, which was used to automate stuff in their mainframe systems.
However, it has a lot of useful applications in the Amiga world. It was originally intended as a so called "IPC", InterProcess Communications language. This means that if two programs has an ARexx "port", you can most likely make them talk to each other using ARexx scripts.
An example of this is that you could write an ARexx script for your DTP program that loads a picture into ImageFX, where you can edit it, and then it's automatically reloaded in the DTP program. You can also do less obvious things such as trigger a backup of your hard drive from your favourite text editor. It all depends on what kind of ARexx support your programs have.
You can also write stand-alone programs in ARexx. Since it's a scripting language, and a rather simplistic one at that, you can't do any GUI or graphics stuff from it. However, a lot of expansion libraries are available, adding the possibility to, for example, create MUI applications and talk to SQL databases. Still, ARexx is a lot more powerful than just ordinary AmigaDOS scripts, thus enabling you to automate a lot of tedious tasks in a number of nifty ways.
If you're interested in ARexx, I recommend you to download ARexxGuide from Aminet.