What problem does it solve?
The Schulte table was originally developed in the 1950s as an attention-training exercise. The idea: keep your gaze fixed at the center of the grid and use peripheral vision to identify numbers as far from center as possible. Skilled performers develop a smooth, wide scan pattern; novices tend to lock onto one quadrant.
Modern cognitive psychologists use it as a measure of sustained attention and peripheral visual span. It's also a surprisingly effective "warm-up" before study or work sessions.