what is their purpose?
The braces are like "arms" (the word comes from Latin).
Their purpose is to support, or to reach-out (like an arm) and provide 'bracing' to the fender, kind of like a 3-point triangle between the fender top attachment to the fork crown (1), the axle (2), and the fender bottom (3); the 3 sides of the triangle are (1) the fork, (2) the fender itself, (3) the fender brace. The triangle is an efficient and strong mechanical design.