From Arduino.cc:

Arduino is an open-source electronics prototyping platform based on flexible, easy-to-use hardware and software. It's intended for artists, designers, hobbyists, and anyone interested in creating interactive objects or environments.

Arduino is a great learning tool. It has been a platform for me to start with then jump into other technologies. I have used the arduino platform to automate certain things around the house. Currently that includes air conditioning, some lighting, soon to be heating, appliance control, and more. For about $30 anyone can get started with arduino. The Arduino IDE  and tools run on Windows, Linux, or Mac OS X. This is a big advantage for me over PIC microprocessors. They provide tutorials and an interfacing with hardware section. Also there is a great, helpful, and friendly community over at the Arduino Forum.

If/when the time comes to move your project off the breadboard and onto something more permanent, you don't have to use a $30 device for each project. You can use a variety of Arduino compatible boards or make your own board with an AVR microprocessor. Here is a short list of Arduino compatible boards:

This is not a complete list, but just a highlight of a select few compatible arduino boards. Some of these boards include XBee sockets. Other are stripped down carrier boards. As mentioned earlier, you can make your own board and design using an AVR atmega328 and a handful of components for less than $10. It is completely up to you.

If/when the time come that you need to use a different ATMega or ATTiny series microprocessor, using arduino has given you a head start on the software. The arduino software give you a nice introduction to microprocessors. From there you can move on to AVR-GCC if you so desire. Atmel (who makes the AVR series) has a wide range of microprocessors with different peripherals.  So if you have any interest in computers, electronics, or programming, check out the Arduino.