The Arduino hardware is a so-called microcontrolling board (Following called „board“). Basically it is a circuit board with many electronic parts around the actual microcontroller. On the edge of the board are many pins with whom it is possible to connect different components. Some of them are for example: Switches, LED's, Ultrasonic sensors, temperature sensors, displays, stepper, etc..
There are different kind of boards, that can be used with the Arduino sofware. Different sized “official” boards, with the official “Aduino” name on it, but also many, mostly cheaper, but equivalent Arduino “fitting” boards. Typical official boards are called Arduino UNO, Arduino MEGA, Arduino Mini, etc. Arduino compatible boards are for example Funduino UNO, Funduino MEGA, Freeduino, Seeduino, Sainsmart UNO etc..
Parts of Arduino
Different equipment
Beside sensors and actuators you need, as a base for quick and flexible experimental setups, jumper cable combined with a breadboard. This way you won't need to solder. Furthermore the LEDs are useful to check the signal output of the board.