To quote their Introduction page:
Arduino is a tool for making computers that can sense and control more of the physical world than your desktop computer. It's an open-source physical computing platform based on a simple microcontroller board, and a development environment for writing software for the board.
It consists of a demo board with (depending on the version) either an Atmel ATMega328, ATMega168, ATMega8 or an ATMega1280. These chips have the Arduino Bootloader burnt into them, which makes it easy to load your own programs onto them (called sketches in Arduino parlance). It also has a crossplatform IDE to allow you to develop for it, the language is based on a subset of C/C++. There are a large number of add-on boards (normally referred to as shields) which allow you to interact with the Arduino or extend its' capabilities.
All of this is open source including the board designs, so you can either buy a premade board, or make your own. The boards are relatively cheap (about £25 for a Duemilanove at the moment) and there is a thriving community of people using/developing/hacking with them.
Here's a picture of one:
