The French drop is a well-known vanish involving sleight of hand. The magician takes a coin or small object between the fingers and the thumb with fingers facing the audience and thumb behind. The palm is face up. We'll assume the object is in the right hand though it could be either. The other hand, in this case the left, approaches and the thumb goes underneath the object while the left fingers close on the object from above. The left hand appears to come away with the object and the space between the right hand finger and thumb is seen to be empty. After a brief pause the magician opens his left hand and the object has disappeared. In some versions the right hand can also be seen empty, leaving no clue as to where the object went.
The secret here is that the left hand never took the object in the first place. As the left fingers closed from above, the right thumb relaxed the grip so that the object fell into the base of the right fingers, while the left hand continues to close just as if taking the object. The right fingers and thumb are left in a position with a small gap between them just as if the left hand has actually taken the object. In skilled hands the illusion is perfect. Now the performer waves the left hand at the audience, misdirecting attention off the right which has finger palmed the object casually pointing at the left hand. Turning to the right the performer again waves the left hand, maybe pattering that the audience should watch the hand closely (more misdirection). At this moment the right hand is behind the body and the performer drops the object in a pocket. Another method is to openly put the right hand in a pocket to obtain a wand or some magic dust, but actually leaving the object behind.
Whichever method is used, the performer is now ready to show the disappearance of the coin or object from the left hand in the most theatrical and fitting way. The right hand can also be shown empty if the above methods have been followed. Since the object is ostensibly taken by one hand, this is known as a take vanish.