To quote the Arduino website, "Arduino is an open-source physical computing platform based on a simple microcontroller board, and a development environment for writing software for the board." Woah, that's kind of a mouthful and I bet you still may be a bit foggy on what Arduino is.
Many people refer to Arduino as a microcontroller. I know I have in the past. This is not quite true. Arduino is a platform that includes a microcontroller along with the means of easily accessing and programming that microcontroller. A microcontroller is a small, typically cheap computer. Most modern electronic devices incorporate one or more of them. When you look at an Arduino board, the microcontroller is the large black rectangular (or maybe square) component.
Arduino is open-source hardware. This means that the creators of Arduino have released a complete set of Arduino's specifications making it possible for anyone to make and sell their own versions of Arduino. Below are several different versions of Arduino. All are made possible because the designers chose to make Arduino open-source.
This is just a small sampling of different types of Arduinos available. They are simply the ones I had laying around. When using a new type of board it is important to orient yourself. Where are the digital and analog pins? Are there extra pins? Is there a reset button? Most types of Arduino clones will have all the standard pins. Some will have extra. These may be more input/output pins or they may be more pins to make serial or i2c communication easier. (I know most of this means very little to you right now, but it will become more clear as you learn more.)It will also be necessary to determine if you need to download anything extra to make them work. The Teensy 3.0 picture above, second from the right, requires you to download the Teensy Loader in order to work.