The Black Hand is the ruling body of the Dark Brotherhood. It is made up of five members: four Speakers (index, middle, ring and little fingers) and a Listener (thumb). Less well known, even by members of the Dark Brotherhood, is that each Speaker also employs a Silencer, which represent the nails of the four fingers.
The Listener hears the commands of the Night Mother and the Speakers enact her will. Each Speaker in turn has a Silencer — a private assassin specifically empowered to do the will of his or her Speaker.
The Silencers are the personal assassins to the members of the Black Hand. Each Speaker (though not the Listener) is entitled to a personal assassin that will eliminate any target they see fit. These highly experienced assassins qualify as members of the Black Hand itself, but their existence is kept a secret from the rest of the Brotherhood. As Lachance says, they represent the nails of each finger of the Black Hand.
According to Lucien Lachance, the Silencers are above the laws of the Dark Brotherhood, and are largely allowed to operate as they see fit. They do not receive orders from their Speakers directly, rather from dead drop orders placed in scattered locations.
This sub-faction can only be joined after the Dark Brotherhood quest: The Purification.