The Question was "the first question in the universe, hidden in plain sight." The Silence believed that "On the Fields of Trenzalore, at the fall of the Eleventh, when no creature could speak falsely or fail to answer, the question that must never be answered would be asked."
The Silence planned to kill the Doctor, whom they believed the only one who knew the answer to the Question. Their first attempt was to frame the Doctor for the destruction of the universe by blowing up his TARDIS, causing the Cracks. This made the Alliance lock him up in the Pandorica, but he was released thanks to his companions. (DW: The Pandorica Opens / The Big Bang) The second attempt was to turn Melody Pond into a weapon to kill the Doctor by Lake Silencio. Both failed, although the Silence were thought to believe the Doctor dead when he allied himself with the Teselecta to fake his regeneration and death. (DW: The Impossible Astronaut, The Wedding of River Song)
Dorium told the Doctor that "silence will fall [when the question is asked]" was a poor translation, and that a better translation would be "silence must fall". Dorium also revealed to the Doctor that the Question was actually "Doctor Who?". (DW: The Wedding of River Song)