Is distance the only measure a launch monitor tests of a golf ball? Yes and no.
Ball spin can tell you a lot more than how far a ball will go, and not just off your driver. If you want more distance off the tee you should test a few golf balls using a launch monitor. This kind of test is the most accurate means of determining which ball will go the farthest with your swing, all things being equal.
However, the launch monitor can tell you a lot about your ball flight, whether the ball will slice or hook, how high in the air it goes and how far it will roll once it hits the ground. These results are measured by the ball spin you impart with the club head based on the launch angle of the ball.
Two golfers with very similar club head speeds can have very different ball spins. There is side spin and back spin; side spin gives you hooks and slices and back spin affects ball height. Too little spin, a common problem with slow swing speeds, results in low distance and ball height. Too much spin can also result in lower distance because the ball can get too high or get very little roll once it hits the ground.
Most golfers generate more club head speed with a wood than with an iron. Lesser golfers with slow swing speeds tend to sweep the ball rather than hit down on it and that sweeping motion gets better results with a wood. Finding a ball that gives this golfer more distance without losing ball height makes sense, since he tends to use his woods on all but the closest shots to the pin.
Golfers who put a lot of spin on their balls will prefer a ball with less spin, a lower trajectory, and control around the green. They tend to have a steep launch angle and more issues with side spin. There over a dozen different brands and models of golf balls that are targeted to this golfer and two or three are likely to work better than the rest. A launch monitor is a good way to figure this out.
Golfers with moderate swing speed can gain 5 to 15 yards off the tee with the right ball, assuming they are using equipment that fits their swing characteristics. A launch monitor can pinpoint which balls deliver.
In short, getting fit for your game involves more than your clubs. Using a launch monitor to help you find the best ball could make as much difference in lowering your score as finding the best driver.