First off you need to know the basic principles behind the idea of a clutch and manual transmission. The engine speed runs at an RPM independent of the vehicle's speed. By selecting the correct gear for both the engine and speed the driver can adjust the both to match driving conditions.
The driver can select a lower gear to force the engine to work harder, and reduce speed, or select a higher gear and let the engine do less work and achieve higher speeds. Reducing speed using the engine is called engine breaking and works well on icy, low traction, or step declines to avoid loss of traction while maintaining a proper speed. This one of the benefits that automatic cars do not have the ability to do in the same manner. A driver could use the lower gears to on the automatic to achieve the same effect yet the automatic transmission could allow the engine into higher RPMs causing damage or could shift higher and lose all of the benefits.
Of course this is the very basic explanation to a manual car, and this is why it is important, the driver is forced to choose the proper gear for the upcoming road and its conditions forcing the driver to look ahead and use their judgement to select the correct gear. That requires more attention, less attention can be given to other devices. Because of the constant road scanning, other hazards are identified earlier and more time to react is had.
And this is why I suggest everyone take the time to learn how to drive stick.