The semi-western forehand grip is where the heel pad and index knuckle of your hitting hand are resting on the fourth bevel of the tennis racket. At 0:10 in the video, you can see a shot of me holding the racket with a semi-western forehand grip, and you can see my heel pad and index knuckle resting on the fourth bevel of the tennis racket handle.
A shortcut to finding the semi-western forehand grip is to place your tennis racket on the ground, and then reach down and pick it back up again. This should get you very close to a semi-western grip, but you should always check to make sure that your hand is resting on the proper bevels.
If you hit with a semi-western grip, your natural contact height will be between your waist and your shoulder. The advantage of a semi-western grip is that it allows you to easily hit both flat and topspin balls, but the tradeoff is that you cannot naturally hit with as much topspin as you could with a full western grip, and you cannot flatten the tennis ball out as easily as you could with an eastern grip.