From "Let's Kill Hitler":
Robot Amy: You killed the Doctor on the orders of the movement known as the Silence, an Academy of the Question.
Robot Amy: Records available.
the Doctor: Question: I'm dying. Who wants me dead?
Robot Amy: The Silence.
the Doctor: What is the Silence? Why is it called that? What... What does it mean?
Robot Amy: The Silence is not a species. It is a religious order or movement. Their core belief is that Silence will fall when the question is asked.
the Doctor: What question?
Robot Amy: The first question. The oldest question in the universe. Hidden in plain sight.
the Doctor: Yes, but what is the question?
Robot Amy: Unknown.
From those statements, we know that the religion of the Silence is one that wants to kill the Doctor because it believes only he can answer the ultimate question, which, according to "The Wedding of River Song", is "Doctor who?"