Definition: "Break" can refer to the amount the path of the putted ball curves, or to the amount the green itself curves or slopes. It's the slope of the green - the contours of the green - that causes the ball to deviate from a straight line, so the two usages of the term are close to identical. If the putting surface is perfectly flat, the ball will roll straight. If there are any contours to green, the ball will "break" away from the straight line.
Examples:
The break of the green is from right-to-left. The putt will break left close to the hole.
