The Arduino is a cheap board which plugs into a computer's USB port and has various digital and analogue I/O pins. You can program the onboard CPU to do stuff, like read from a sensor and flash an LED if the value goes over a threshold, and send a warning message over the USB port back to your computer, which might send a twitter message (for example). You do not need to have the Arduino plugged into a USB port though, it can run off batteries, which makes it great for hobby robotics.
Due to the flexibility of the Arduino platform, a strong online community has grown up around them (and similar devices).
Low-cost X-Plane Control PanelUsing one Arduino Uno, I built a physical control panel for the XPlane flight simulator. It is quite simple inside, using just 6 digital inputs (the switches), 2 analogue inputs (the sliders) and two digital outputs (the LEDs) of the Arduino.
Weather Station ReceiverI bought a few of these 433 MHz radio receivers on eBay for a couple of pounds, with the intention of receiving the signal broadcast by my outdoor weather station sensor, which sends temperature and humidity data to the base station indoors (which just displays it, and has nothing helpful like a USB port for logging the data).
This project is ongoing. I have successfully received the signal and cracked the code, but at the moment the receiver range seems to be very limited (1 metre) and I am figuring out a way to improve it. Once it works reliably, the plan is to program an ATtiny85 to act as a signal decoder, which would then send the decoded data over serial to a Raspberry Pi, for logging and to send the data across the internet.