It uses transistors to basically switch the motor leads from +supply/gnd for current flow in one direction, to gnd/+supply for current flow the other direction to make the motor spin the other direction.
Depending on how big your motor is, what voltage/current is required, you may be able to use this part, or find a beefier part, or use discrete transistors with a chip like this to drive/control the transistors. You may be able to use an existing motor shield for this.
What will the source for your HIGH/LOW signal? Reading that from a digital pin is usually the easist part of the project, such as from a mechanical switch.
KE7GKP:
So you want forward/stop/reverse control based on inputs from several transducers. Yes, that would require a micro-controller and an H-bridge, (or a transistor and a relay). But a simple H-bridge can be constructed from four jelly-bean transistors and is quite a simple circuit.