The idea of the past being malleable helps to keep the power structure intact in Oceania. The notion of being able to retell historical narratives so that they reflect that the power of Big Brother is something out of the inevitability of the past's realization is used to create legitimacy. It is easier for any political authority to use the past in order to justify it because individuals will be more likely to accept its authenticity. For example. Hitler's appeal to a historical condition of Germany that allows for "great leaders" and "superior people" to emerge was justified through a mutability of German identity and the historical lineage of being German. In this light, individuals were able to believe, falsely, that Nazi values had a historical basis. In this light, the "mutability of the past" helped to bring present legitimacy.
Orwell's novel is essential about power and control--specifically, the frightening prospect of a totalitarian government controlling every aspect of society. One of the most important means of control exerted by Big Brother is that over what is known about one's history.
Winton's work in The Ministry of Truth is to "rectify" history in order to make Big Brother and IngSoc appear in a favorable light. This is very clear in Part One, Chapter Four. One example is Winston's creation of Comrade Ogilvy, who though fictional will "exist" due to Winston's account of him. The Party needed a hero and Winston manufactured one. Another is Winston's realization that while the Party is pleased to announce that the chocolate ration has increased, he knows that it has actually been reduced.
Essentially, the power to control information about the past allows the government to control the present. If you are sure that something happened--perhaps even witnessed it yourself--but no one acknowledged it, did it really happen? History is only relevant because we choose to make it significant. Big Brother goes one step further and manufactures history. The Party wipes clean any reference to what is not favorable and creates lies to suit its purposes.
Goldstein attempts to explain this in "The Book" in Part Two, Chapter Nine, but fails to articulate the full importance and significance of the mutability of the past and the essence of "doublethink." He can explain the "how" but not the "why."
I understand the phrase "mutability of the past" as Big Brother's way of rewriting historical events that are negative or in conflict with the government's view of present life. By falsifying employee production figures, outcomes of military conflicts, and other facts deemed counterproductive to the morale of the people, Big Brother effectively mutes past mistakes and embarrassments. By controlling all information, the Party is able to rewrite all history--even the most recent--to reflect a positive view of current events. Only the very old can remember what really happened before Big Brother began the revisions, and they are looked upon with skepticism by the young. Since Party members are forbidden to read or consider what their own memories may recall, they readily accept Big Brothers ever-changing facts and figures.
Winston talks of the "mutability of the past" since he is one of the Party members who constantly works to change it. No one actually knows what the truth is since the past is mutated and changed so much through the use of memory holes and rewritten or "rectified" histories. One example is the photo that proves the trio (Rutherford, et al) who hung out at the Chestnut Tree Cafe before being "vaporized" were innocent. The photo showed up a few years after the trio were unpersons, and required Winston's department to "rectify" the past. However, proof does turn up from time to time that the Party alters the past to suit its purposes. The Rectification department also creates fictional characters as well as completely erases people from the past. This is why Winston was so intrigued with the past and the examples of the past such as the diary, the paperweight, and the rhymes about the church bells that he learned from Mr. Charrington. Another example of the past being changed is the fact that one week the chocolate ration was 30 grams and the very next week is was lowered to 20, but the telescreens celebrated the fact that it was "raised" to 20 grams. Winston often wonders if he is the only one who realizes the truth.