In The ShowEdit
The Silence first appeared in Series 6 Premier 'The Impossible Astronaut/Day of the Moon', where the Doctor travels with his companions Amy Pond, Rory Williams and River Song to 1969, after they receive co-ordinates from the Time Lord, just before his death. While there, they discover a species of tall, suit-wearing aliens, similar in appearance to Roswell Greys. These aliens have the ability to manipulate electricity, brainwash Humans into doing their bidding and cause creatures to forget them went they looked away. During the second part of the episode, the Doctor interrogated one of these creatures that had been wounded by FBI agent Canton Delaware III, trying to find out his new enemies name. It answered "Silence, Doctor. We are the Silence".
The Doctor defeated the Silence by having Delaware record the Silence giving a command to have them killed on sight and broadcasting it at the moment Neil Armstrong landed on the Moon. This caused people to attack and kill the Silence on sight. A short while after this, the Doctor found out that during the events Amy had been kidnapped and taken away to give birth to a child, as she had claimed to be pregnant during the events of the Impossible Astronaut. After locating her and captor, he learnt from their leader Madam Kovarian that the Silence were actually part of a religion, hell-bent on killing him. She, of course, was part of the Silence and was training Amy's daughter, Melody Pond, to eventually execute him.
In the series finale 'The Wedding of River Song', the Doctor learnt from Dorium Maldovar that the Silence were trying to kill him to stop a prophesy that predicts that he will die on the planet Trenzalore in a battle that wipes out all life in the Universe. In order to survive this, the Doctor hid in a Teselecta and faked his death. The Doctor then proceeded to remove himself from history, to make sure the Silence would not attack again.
In the 2013 Christmas special, The Time of the Doctor, the Silence are reviled to be part of the Papal Mainframe, a church that orbited the planet Trenzalore and protected it from hostile threats. They received their name when the Mother Spurious Tasha Lem decided to dedicate the religion to Silence, thus giving their name. It was also reviled that Kovarian broke off part of the church to try and assassinate the Doctor. During the siege of Trenzalore, the Silence became the Doctor's allies and fought with him against the Daleks and various other enemies.
In The ModEdit
Silence are found on Trenzalore. When the player approaches they released a blinding chain of lightning. They are very tall and have 20 health.