A H-bridge is an electronic circuit that switches the polarity of a voltage applied to a load. These circuits are often used in robotics and other applications to allow DC motors to run forwards or backwards. (Adapted from Wikipedia)

This monster of a diagram actually isn't too bad when you take a closer look. The pins in the upper right and lower left corners (logic and motor power) must always have power for the circuit to work (they supply power to the internal chip computer and the motors, respectively). The enable pins (upper left and lower right) are connected to digital output pins on the Arduino and dictate whether the motors can spin or not (if motor 1's enable is LOW, it won't spin no matter what, and the same applies to motor 2). The leads of the DC motors must be connected to their output pins (motor 1 has both leads to motor 1 output pins, and the same applies to motor 2). All 4 signal pins (motor 1 A, motor 1 B, motor 2 A, and motor 2 B) must be connected to digital output pins on the arduino. These are a bit trickier, but they dictate the polarity of voltage and therefore the direction of rotation. The A and B pins must be a HIGH/LOW pair for the motor to spin—supplying HIGH to both or LOW to both won't make the motor spin; but having A be HIGH and B be LOW will make the motor spin in the opposite direction than if B was HIGH and A was LOW.