Speakers of the Black Hand are the third most powerful people in the Dark Brotherhood, after Keeper and Listener. In Oblivion, the Black Hand is compared to an actual hand, the four fingers including the Speakers and the thumb being the Listener -makes the biggest mark; the one who gives orders to Speakers who give orders to their Silencers.
In Skyrim, if the Dragonborn decides to join the Dark Brotherhood and becomes the Listener, they will also be performing duties of the Speaker.
Dead Drop Orders
Throughout the Dark Brotherhood questline, the Hero advances in rank only to become Lucien Lachance's Silencer, to which they gain "Dead Drop" orders. However, only the first two orders are real, resulting in them killing Speakers and other Silencers. In later quests, they become the Listener (after meeting with the Night Mother).