Rather than a specific race, The Silence are a religious order. Their agents on Earth have been there since before the dawn of mankind, directing human evolution. Through the use post-hypnotic suggestion, The Silence make people who see them instantly forget their existence. After an incursion with The Eleventh Doctor, Amy, Rory and River Song, the Silence became known to mankind, temporarily halting their plan.
They used their agent Madame Kovarian to kidnap a young Melody Pond and raised her as the Doctor’s perfect assassin - otherwise known as River Song. In a time-shifting and parallel universe-creating ruse, the Time Lord managed to sabotage the plan.
Upon receiving an impossible message, the Eleventh Doctor made his last journey to Trenzalore where he found his old friend Tasha Lem was working alongside the Silence. Here he discovered they blew up his TARDIS and created the very cracks in the universe which had followed him around (and from which the Time Lords would come calling). Despite trying to kill the Doctor, the Silence ended up as part of a Destiny Trap - "You can't change history if you're part of it," claimed the Doctor. The Silence helped ensure the Daleks didn't win the Siege of Trenzalore, thus fulfilling their prophecy.