Handlebars

The handlebars (along with the front tire and rider of the bike) help steer the bicycle.  The steering angle of the bicycle is caused by the rotating steering axis.  Wikipedia has the equation for the actual kinematic steering angle: 

( is the kinematic steering angle,   is the actual steering angle, and   is the caster angle of the steering angle.)

Steering the bike is an important part of the bike because it helps the rider stay upright and get where they need to go.