Once proper contact is established, the "lifting" motion, is very similar to a boxing upper cut punch. In the animation watch Gustavo Kuerten drive his bent arm upward from his shoulder. This motion is what creates so much power on the foreand. The racket holds back while the entire bent arm drives upward from the shoulder. This creates tremendous force on the ball.
In the image below, notice how Guga's contact point resembles that of a boxer's "contact point" when his glove is on his opponent. From this position a tremendous amount of force can be generated from the shoulder in an upward punching motion. Notice how Guga's modern grip puts the palm of his hand under the handle. This grip, with the hand more under the handle, lets you lift upward more powerfully.
I think this animation really shows how the modern forehand connects the ball to the body in a way that the "classical forehand" never could. Instead of an eastern grip (or continental) which puts the hand behind the handle, the modern grips put the handle more under the handle so you can get a powerful upward thrust of the arm. The "old way" of trying to swing forward on an even plane toward the target just can't complete with this powerful lifting thrust of the arm and shoulder.
To get a sense of how this upper cut motion is fast and powerful - really a muscular "thrust" of the arm and shoulder - check out this video of boxing uppercuts to see how much force it generates.
An incredible teaching tool for this is pictured to the right. Take a board and put it on an incline. Put your racket and flat on the board in a proper leveraged contact position. Press your racket into the board and then lift your arm and racket together in the upper cut motion. By pressing into the board as you lift upward, you should feel your shoulder pressing your hand and racket into to the board as simultaneously lifts upward. This is the power source of the modern forehand.
Unfortunately, the Muscle Memory Board is no longer being produced, but you can read about the creator here. However, just get a long board, put it at an incline against a wall or the fence, and you'll get the same results.