Parsons is a seemingly ordinary, working-class man who is deeply devoted to the Party and its ideology. He is a neighbor of Winston Smith and is constantly enthusiastic about Big Brother and the Party's policies.
He is arrested by the Thought Police for thoughtcrime, specifically for dreaming that he is betraying the Party. The dream is presented as evidence of his "thoughtcrime," even though it is clearly unintentional and a result of his deep-seated fear of the Party.
The arrest of Parsons highlights the oppressive nature of the totalitarian regime in Oceania. The Party is able to control every aspect of life, including people's thoughts and dreams. Even someone who is seemingly loyal and supportive of the Party can be targeted for thoughtcrime.
Ampleforth is a different character in *1984*. He is a poet who works for the Ministry of Truth and is responsible for rewriting historical records to fit the Party's narrative. While he is not explicitly arrested, he is sent to the Ministry of Love for a period of time for his "crime" of using the wrong word in his work. This demonstrates the Party's relentless pursuit of control, even over seemingly insignificant details.