The Question

The Question was, according to the Teselecta's computer, "the first question in the universe, hidden in plain sight." It was the organising principle for religious movement known as the Silence. They thought that "silence will fall when the Question is asked".

More specifically, the Silence believed that

... on the Fields of Trenzalore, at the fall of the Eleventh, when no creature can speak falsely or fail to answer, the Question that must never be answered will be asked.Dorium Maldovar

The Silence planned to kill the Doctor, whom they believed the only one who knew the answer to the Question. (DW: Let's Kill Hitler) Their first attempt was to frame the Eleventh Doctor for the destruction of the universe by blowing up his TARDIS, causing the Total Event Collapse. This made the Alliance lock him up in the Pandorica. (DW: The Pandorica Opens) The Doctor was released by his companions and his future self and restored the universe with the Pandorica he had been trapped inside. (DW: The Big Bang) The second and third attempts were to turn Melody Pond into a weapon to kill the Doctor in 1938 Berlin and later 2011 Lake Silencio. Both failed, although the Silence thought the third attempt successful. Unbeknownst to the Silence, he had used the Teselecta to fake his death at Lake Silencio. (DW: The Impossible Astronaut, Let's Kill Hitler, The Wedding of River Song)

Dorium Maldovar told the Doctor that "silence will fall when the question is asked" was a poor translation. A better translation would be "silence must fall...". Although the Teselecta's databases were unable to identify the Question, Dorium claimed to know it — though it was unknown how he came by the knowledge. According to him and no other sources, the Question was actually "Doctor who?" (DW: Let's Kill Hitler, The Wedding of River Song), indicating that the answer to the question is the Doctor's name.