An SVM draws the biggest possible gap between two groups, so new points are easy to classify correctly.
Imagine it like this: Picture red and blue marbles scattered on a table, and you have to draw a single line to separate them. You wouldn't draw it right next to the red marbles, or right next to the blue ones — you'd draw it in the middle, as far as possible from both groups. That gives new marbles the best chance of landing on the right side.
Examples:
So? By keeping the largest possible "safety margin" between groups, SVMs make fewer mistakes on new, borderline cases.