First off what the heck is Arduino?
"Arduino is a physical computing platform based on a simple I/O board and a development environment that uses the Wiring library to simplify writing C/C++ programs that run on the board. Arduino can be used to develop stand-alone interactive objects or can be connected to software running on a computer (e.g., Adobe Flash, Processing, Max/MSP, Pure Data, SuperCollider). Currently shipping versions can be purchased pre-assembled; hardware design information is available for those who would like to assemble an Arduino by hand."
In other words Arduino is an easy to use, hobbyist programmable little computer that can be used for all sorts of projects from interactive lights to robots.
The best way to learn about Arduino and the possibilities is with this inexpensive guide written by one of the people who created Arduino:
After reading the book you'll want to dive in and try out the examples yourself! The confusing part is assembling all of the components you'll need. This kit will give you a great start and can be used to create the examples from the book and beyond: