Do you ride the piglet known as the Suzuki DR-Z400/S/E bike?
 
Well, like bikes of this era, they use a conventional fork, meaning the small tubes (the stanchions) are on the top, and the bigger diameter ones are near the wheel. This older design makes an inherently less rigid fork than modern upside-down ones.
 
What is the point of a fork brace? A fork brace or fork stabilizer prevents twisting in the forks by adding some rigidity on the separate lower legs, linking them together.
 
If you ride your piglet hard, you might notice a wobbly feeling at speed or less than direct control between the handlebar and the wheel.
 
Stiffen that wimpy front end, and be more confident on and off the road!
 
More responsive to steering input.
Reduces low and high-speed wobbles.
Improves stability in tight cornering.
Decreases sensitivity to rough surfaces road.
 
A brace provides better stability and overall better handling of your bike. This particular model also sits low enough not to touch the fender too easily.