When you create or prototype a circuit, you face a messy collection of wiring. How can you document your circuit so everything is neat and organized? You can take a picture of it. But when you want to change it you need to take another photo. Also, a photo may not show all the detail needed to for someone to recreate your invention. What else can you use?
You could, possibly, use a drawing program. But circuits often require special symbols and connections to be really clear to the read. Its also really difficult to draw symbols. If you don't have a library of symbols, you spend a lot of time making symbols rather than your circuit.
Fritzing is an opensource program that lets you take your wiring design for an Arduino project (or most anything involving electronics) and turn it into a nice looking graphic for others to see. The program has built in clip-art like objects like the Lilypad arduino board and other sensor components.
Simply drag-and-drop the components onto a canvas and connect the terminals with lines that represent wires. Wires can be color coded to represent red (power), black (ground), and other leads like sensors.
The nice thing about this program is that it lets you make and export highly visual diagrams of your projects without having to know the formal symbols to draw a electronic schematic. The diagrams gives a learner who may have not had any exposure to schematics a way to under how to connect the circuit.
Documentation is important in any making project, especially if you want to revise it later or have your audience build on your design.
Fritzing if a free download and is available on Windows, Mac OS, and Linux. It easy and simple to use. After about 10 minutes of experimentation, I was able to create this simple diagram on how to hook up a common LED with resistor to an Lilypad board.