The clavichord was invented in the 14th century and is a direct ancestor of the piano. Unlike the harpsichord that plucks the string when a key is depressed, the clavichord has a brass upright, or tangent attached to the end of the key that hits the string when the key is depressed. these tangents are shown in close up in the photo to the left. This difference in action makes the clavichord capable of changes in levels of volume, but the range is not very large. It is an instrument that played at its loudest could never be heard in a concert hall, so it was and still is an instrument for the home. Bach's piece is in a minor key, and unlike other pieces written in rondo form of the time, this one is rich in feeling and emotion, even sadness, as it depicts Bach's feeling of saying farewell to an old friend.
If you watch the video of the piece closely, you'll see the performer occasionally move a finger up and down on a key. This is a unique attribute to the clavichord, the ability to play vibrato on a keyboard instrument. It was a common part of clavichord technique at the time as there is a German word for it, bebung.