Arduino is an open-source hardware prototyping platform. It is widely used today in electronics projects because it is easy to learn, simple in design, well documented and cheaper. We call it platform because it is both hardware circuit as well as piece of software, the IDE. It also has its own programming language. All these open-source components collectively makes the Arduino platform.
Bit of History:
It all started at IDII, Ivrea, Italy in 2003 when some students at the institute started working on creating a low cost prototyping tool for digital projects. Arduino's sturdy design tells us that it is created by design people and not hardcore electronics guys. You know how bad they are :P