What is the purpose of having Big Brother and Goldstein not appear in the novel, but showing such an influence on the people?
Neither Goldstein nor Big Brother are living entities. They are representative of ideas. Big Brother is the government's icon used to terrify people into conformity by making people aware that the government is watching them constantly, but at the same time, give people the idea that the one watching them is watching out for them, like a big brother might. Goldstein is not a real person in the story either. Goldstein was a character the government created to help them sift out the dissidents. Goldstein was supposedly the leader of the resistance and those who wanted to resist the government would rally in the name of Goldstein because people thought Goldstein had created the Brotherhood and written its manifesto. Both Big Brother and Goldstein are necessary to the story because the government controls everything people think, do, or say and it is through these two characters that this control exists. The government uses these two icons to manipulate people.
Big Brother and Goldstein serve as symbols in 1984: Big Brother represents absolute power, and Goldstein serves as a scapegoat. Both are fundamental to dictatorships. In having Big Brother appear only in the posters hung throughout Oceania, Orwell creates an awesome, awful presence in society--that of the omnipotent and allegedly benevolent dictator. Big Brother is the government that intrudes upon and controls every aspect of the individual's existence. So that the people have an outlet for their negative emotions and are therefore more easily controlled, the government gives them Goldstein as a target for their hatred. These two non-people exemplify concepts essential to dictatorships: that the people must feel safe, even though the government denies them their fundamental freedoms, and that the people must be inclined to blame someone other than the government for their problems.
Goldstein is a christ like figure in that he is never actually seen by today's time yet he offers hope for people. And Big Brother serves as sort of a satan type figure in that he seduces you into believing he is good i order for you to work towards his beliefs. "Big Brother" serves as a misleading name to his true nature. Goldstein is the figure who offers hope for those struggling to rebel against Big Brother. Also they even mention the book that the Goldstein believers/supporters read in order to know more about what he is for and to gain a general wisdom about their society and how Big Brother traps others into his scam. This book symbolizes the bible.