Most tennis players choose a tennis racquet with great care, but many don't realize that their racquet's stringing may have a more profound effect on their game than their carefully chosen frame.
At a minimum, every tennis player should understand the basic trade-offs among comfort, power, control, and spin in relation to string tension. Any decent tennis racquet will have a recommended range of string tensions, for example 58 to 68 pounds. When we talk about low or high tension, it makes sense to confine ourselves within no more than 10% outside this range, because at extremely low tensions, some of the normal correlations break down.
Within the recommended tension range for a given set of strings, lower tensions offer significantly less stress on the arm and slightly more power, and higher tensions offer significantly more control at a given level of topspin.
Topspin improves control by making the ball fall faster as it flies forward. For a swing at a given speed and upward angle, some strings produce more topspin at lower tensions, some at higher tensions, with differences on the order of 10% or less. If a player's swing brushes the strings up the back of the ball while also smacking it forward, as most advanced players' swings usually do, a faster swing increases both spin and power. The reduced power and increased control of higher tensions allow players to swing faster without hitting long, and when they swing faster at a given upward angle, they produce greater topspin.
Looser strings hit farther in part because the ball stays on the strings longer, and because on most swings the racquet tilts upward and rises as it moves forward, a ball that stays on the strings longer leaves the racquet on a higher trajectory. The key to understanding the other reason that lower string tensions yield more power is to compare the energy return offered by the strings to that offered by the ball.
If you read the official rules of tennis, you'll find a section that specifies that the ball, when dropped on concrete from 100 inches, shall rebound to between 53 and 58 inches. In any collision, some energy is lost to vibration and friction, and in the case of a tennis ball, a huge amount is lost in deforming the ball's materials. As the ball hits the concrete, part of it compresses, and the rubber stores some of that energy, which is then released as the ball uncompresses. If all of that energy were stored with perfect efficiency, the ball would bounce right back to 100 inches (in a vacuum), but as a tennis ball is designed, it dissipates around 45% of that energy. A "Superball" is better at storing its compression energy, and it will bounce back much higher when dropped from the same height, but a ball that could bounce back to 100% of its original height is still a physical impossibility. If such a ball were possible, it would bounce forever.